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Full text of "Static load tests for through-fastened metal roof and wall systems"

STATIC LOAD TESTS FOR THROUGH-FASTENED 
METAL ROOF AND WALL SYSTEMS 



By 

JONATHAN SABIA KREINER 



A DISSERTATION PRESENTED TO THE GRADUATE SCHOOL 

OF THE UNIVERSITY OF FLORIDA IN PARTIAL FULFILLMENT 

OF THE REQUIREMENTS FOR THE DEGREE OF 

DOCTOR OF PHILOSOPPr^ 

UNIVERSITY OF FLORIDA 

1996 . , 



UNIVERSITY OF FLORIDA UBRARES 



J 



©Copyright 1996 

by 

Jonathan Sabia Kreiner 



TABLE OF CONTENTS 

Eage 

SYMBOLS AND ABBREVIATIONS iv 

ABSTRACT x 

CHAPTERS 

1 INTRODUCTION TO STATIC LOAD TESTING 1 

1.1 General 1 

1.2 Research Objectives 3 

2 TENSILE TESTS.. 8 

2.1 General 8 

2.2 Procedure 8 

3 STANDARD PULLOVER TESTS 11 

3.1 General 1 1 

3.2 Procedure 1 1 

3.3 Results 12 

4 SIMULATED TESTS 26 

4.1 Components 26 

4.1.1 Concentric Loading 26 

4.1.2 Eccentric Loading 29 

4.1.3 Revised Apparatus (Load Cell Development) 29 

4.1.4 The Strain Gage Test 31 

4.2 Systems 34 

4.2. 1 Introduction To The Vacuum Box Test 34 

4.2.2 Apparatus Design And Construction 35 

4.2.3 Test Methods And Data 37 



m 



5 PULLOVER THEORY 99 

5.1 General 99 

5.2 Uniaxial Tension 100 

5.2.1 AISl Specifications (Section E4.4.2) 100 

5.2.2 The Actual Condition 101 

5.3 Biaxial Tension 107 

5.3.1 Biaxial Stresses 107 

5.3.2 Concentric Loading 1 1 1 

5.3.3 Eccentric Loading 1 14 

5.4 Pullover Strength And Steel Strength 122 

6 FIELD INSPECTIONS 142 

6.1 Existing Systems 142 

6.2 Catastrophic Failure 142 

7 CONCLUSIONS AND RECOMMENDATIONS 165 

7. 1 Reduction Factors For The Standard Test 

And Equation E4.4.2.1 165 

7.2 Summary Of Test Data And Theoretical Data 169 

7.3 Recommendation For The Standard Pullover Test 171 

7.4 Sample Problems 173 

REFERENCES 192 

BIOGRAPHICAL SKETCH I93 



IV 



SYMBOLS AND ABBREVIATIONS 

Aa - Longitudinal Projected Area Of Hole Drilled From Fastener 

Ap - Transverse Projected Area Of Hole Drilled From Fastener 

a - Width Or Length Dimension 

b - Width Or Length Dimension 

C - The Ultimate Strength To Yield Strength Ratio For Steel 

c - Constant 

d - Depth 

da - Longitudinal Projected Distance For Stress Distribution 

dfi - Transverse Projected Distance For Stress Distribution 

^ ■■ ■: iAJ 

dj - Projected Distance For Stress Distribution 

^ . I 'I '■■'■■ '■ 

f//, - Hole Diameter ^ ^' 

dy, - Washer Diameter By Definition Of AISI Specifications 

E - Modulus of Elasticity 

Eea - Longitudinal Elastic Modulus 

Epa - Longitudinal Plastic Modulus 

Eep - Transverse Elastic Modulus 

Epp - Transverse Plastic Modulus 

Eeamax " Elastic Modulus For Shortest Longitudinal Span 



■'eamin 



Elastic Modulus For Longest Longitudinal Span 
Eepniax " Elastic Modulus For Shortest Transverse Span 
Ee^n - Elastic Modulus For Longest Transverse Span 
Epamax " Plastic Modulus For Shortest Longitudinal Span 
Epamin " Plastic Modulus For Longest Longitudinal Span 
Eppnua - Plastic Modulus For Shortest Transverse Span 
Eppmin - Plastic Modulus For Longest Transverse Span 
Fa - Longitudinal In-Plane Tensile Stress 
Fp - Transverse In-Plane Tensile Stress 
Fau - Longitudinal Ultimate In-Plane Stress 
Fen - Longitudinal In-Plane Yield Stress 
F^. - Transverse In-Plane Yield Stress 
Fcmiax - In-Plane Tensile Stress For Shortest Longitudinal Span 
Famin " In-Plane Tensile Stress For Longest Longitudinal Span 
Ffimax - In-Plane Tensile Stress For Shortest Transverse Span 
Ffimin - In-Plane Tensile Stress For Longest Transverse Span ,.-• 

fp - Actual Bending Stress 
Fp - Allowable Bending Stress 
Fe- Stress For Longer Span In A Uniaxial, Eccentric Loading Condition 



VI 



Fu - Ultimate In-Plane Stress 

Fui - Ultimate In-Plane Stress By Definition Of AISI Specifications 

/ - Actual Shear Stress 

Fv - Allowable Shear Stress 

Fy - Yield Stress 

/ - Moment of Inertia 

/ - Length 

la - Longitudinal Span Length For Biaxial, Concentric Loading 

Ip - Transverse Span Length For Biaxial, Concentric Loading 

lamax " Shortest Longitudinal Span Length 

lamin " Longest Longitudinal Span Length 

Ipmax - Shortest Transverse Span Length 

Ipmin - Longest Transverse Span Length 

M - Moment 

Pnov - Pullover Strength By Definition Of AISI Specifications 

Pu - Ultimate Axial Strength 

qo - Distributed Load 

Q - Shear Flow 

R - Reaction At Support 



vu 



S - Section Modulus 

t] - Thickness By Definition Of AISI Specifications 

V- Shear 

w - Distributed Load 

W- Displacement 

a - Angle Of Deflection For Span a (Biaxial, Concentric Loading) 

(Xu - Ultimate Angle Of Deflection For Span a (Biaxial, Concentric Loading) 

a„uix - Angle Of Deflection For Shortest Longitudinal Span 

amin - Angle Of Deflection For Longest Longitudinal Span 

o^maxu - Ultimate Angle Of Deflection For Shortest Longitudinal Span 

(Xminu - Ultimate Angle Of Deflection For Longest Longitudinal Span 

/)- Angle of Deflection For Span b (Biaxial, Concentric Loading) 

/?„ - Ultimate Angle of Deflection For Span b (Biaxial, Concentric Loading) 

fimax - Angle Of Deflection For Shortest Transverse Span 

^min - Angle Of Deflection For Longest Transverse Span 

^maxu - Ultimate Angle Of Deflection For Shortest Transverse Span 

^minu - Ultimate Angle Of Deflection For Longest Transverse Span 

S - Deflection 

A - Deflection 

viii 



Aca, - Ultimate Defelction For Longitudinal Span 

A^ - Ultimate Deflection For Transverse Span 

Aamaxu " Ultimate Defelction For Shortest Longitudinal Span 

Aaminu " Ultimate Defelction For Longest Longitudinal Span 

Apnuvcu - Ultimate Deflection For Shortest Transverse Span 

Afiminu - Ultimate Deflection For Longest Transverse Span 

£ - hi-Plane Strain 

Sa - Longitudinal In-Plane Strain 

€p - Transverse In-Plane Strain 

£a), - Longitudinal In-Plane Yield Strain 

£py - Transverse In-Plane Yield Strain 

£au - Ultimate Longitudinal In-Plane Strain 

£/)u - Ultimate Transverse In-Plane Strain 

£amax " In-Plauc Strain For Shortest Longitudinal Span 

€amin " hi-Planc Strain For Longest Longitudinal Span 

^amaxu " Ultimate In-Plane Strain For Shortest Longitudinal Span 

^aminu " Ultimate In-Plane Strain For Longest Longitudinal Span 

^yftnox - In-Plane Strain For Shortest Transverse Span 

^flmin - In-Plane Strain For Longest Transverse Span 

ix 



^Pmaxu - Ultimate In-Plane Strain For Shortest Transverse Span 

£^nu - Ultimate In-Plane Strain For Longest Transverse Span 

^amaxy " In-Planc Yield Strain For Shortest Longitudinal Span 

£aminy " hi-Plane Yield Strain For Longest Longitudinal Span 

^Pmaxy " In-Plane Yield Strain For Shortest Transverse Span 

Spminy " In-Plane Yield Strain For Longest Transverse Span 

^ - Angle Of Failure Mode Generated From Biaxial In-Plane Tension 

6- Angle Of Deflection 

Oa - Angle Of Deflection For Span a (Uniaxial, Eccentric Loading) 

dp - Angle of Deflection For Span b (Uniaxial, Eccentric Loading) 



Abstract of Dissertation Presented to the Graduate School 

of the University of Florida in Partial Fulfillmemt of the 

Requirements for the Degree of Doctor of Philosophy 

STATIC LOAD TESTS FOR THROUGH-FASTENED 
METAL ROOF AND WALL SYSTEMS 

By 

JONATHAN SABIA KREINER 
AUGUST 1996 

Chairman: Dr. Duane Scott EUifritt, P.E. 
Major Department: Civil Engineering 

Self-drilling screws are used for attaching roof and wall panels to 
structural framing and are often subjected to tensile loads caused by negative 
wind pressures. A failure mode often associated with this loading condition 
is pullover, which occurs when a fastener pulls through the sheet but remains 
attached to the structural framework underneath. 

The American Iron and Steel Institute (AISI) has developed several 
standard tests for pullover. Previous research at the University of Florida has 
focused on one particular test and has found that it is unconservative, 
providing fastener load capacities 2.5 times greater than load capacities 
measured in an actual installation. Given this discovery, a proposal was made 'J 
to AISI in 1 993 requesting ftuther study of pullover and its effects by testing 

xi 



a wider range of variables and providing a reduction factor for the standard 
test. The proposal was approved and research began in May 1 994. 

hi order to determine the reduction factor for the standard test, simulated 
tests were performed in addition to the standard tests. While initially using 
the simulated testing apparatus, many difficulties were encountered and 
adjustments were made to improve the simulated data. From these 
adjustments a new and improved apparatus for the simulated test (the vacuum 
box test) was developed and proposed to AISI in the summer of 1 995. The 
proposal was approved and a new series of simulated tests were included. 
Rather than testing single components alone, this new series included system 
testing, which modeled the actual conditions more realistically. For these 
reasons, the system tests proved most valuable when determining reduction 
factors for the standard test. 

The purpose of the research was to provide a better understanding of 
pullover. The first approach was to determine a reduction factor for the 
standard test specified in the AISI Cold Formed Steel Design Manual. The 
second approach was to develop both theoretical and empirical methods for 
designing through-fastened metal panel systems that resist pullover. 



xu 



CHAPTER 1 
INTRODUCTION TO STATIC LOAD TESTING 



1.1 General 

Self-drilling screws are used for attaching metal roof and wall sheets to 
structural framing (Figure 1-1). These screws are often subjected to tensile 
loads caused by negative wind pressures. Two failure modes associated with 
this loading condition are pull-out and pull-over. Pull-out is a fastener's 
resistance to pulling out of the heavier framework undemeath the sheet, and 
pull-over occurs when a fastener pulls throu^ the sheet, but remains attached 
to the heavier framework. The primary focus of this discussion is pull-over. 

The American Iron and Steel Institute (AISI) has developed several 
standard tests for pull-over. One test is simple to conduct and requires only 
small amounts of sheet material. A schematic of this Standard Pull-Over Test 
is shown in Figure 1-2. This test does not attempt to simulate the action in a 
real installation. In an actual building, the sheet is perpendicular to the screw 
axis and in a state of biaxial membrane tension when pulled in a direction 
parallel to the axis of the screw. This behavior differs from that of the 



Standard Test, which provides the same loading condition, but does not 
provide the same support conditions (Figure 1-1). A member used in the 
Standard Test has a stable initial support condition, which remains stable 
throu^out the loading process. This has greatly affected the actual load 
capacity of a given member. In fact, previous research at the University of 
Florida has shown that the Standard Test produced a load approximately 2.5 
times greater than the loads recorded from the test that simulated a real 
installation. For this reason, the Standard Test may be very un-conservative 
when used to determine the number of screws required to hold down a metal 
sheet subjected to a given wind load. 

Previous research was performed only on one roof sheet configuration, 
one gauge, one steel grade, one screw position, and one simulated sheet span. 
In order to accurately assess the differences between a Standard Test and a 
simulated building test, many more simulated building tests must be 
performed. For this reason, an expanded program of testing has been 
established. This report describes the details of the research and provides 
data relating to the effectiveness of the simulated test. One objective was to 
be able to predict the performance of a through-fastened sheet in a real 
building by performing the Standard Test and applying a reduction factor. 



The reduction factor will depend on testing a wider range of variables than 
those previously tested (Table 1-1). 

All previous simulated tests have been set up to produce perfect axial 
tension on the screw. This simulates the attachment of a continuous sheet at 
an interior support, which is probably the most ideal of conditions (Figure 1- 
3). In a real installation, many screws are eccentrically loaded and are more 
likely to fail before a concentrically loaded screw. The Standard Test is 
concentrically loaded, which tests the ideal state of attachment and is im- 
conservative. Therefore, in order to obtain a more conservative reduction 
factor, several of the simulated tests included eccentric loadings (Figure 1-4). 

1 .2 Research Objectives 
The primary objective was to determine a reduction factor for the Standard 
Test. However, a favorable objective was to revise the Standard Test 
because the current testing procedure does not accurately model an actual 
installation. Section E4.4.2 in the 1996 Draft AISI Specification provides a 
standard equation for calculating pullover. Both the equation and the 
Standard Test provide the same pullover values for a given system because 
the equation was derived from a free body diagram of the standard testing 



apparatus. Therefore, it was also necessary to revise Section E4.4.2 by 
providing the appropriate design criteria for pullover. This was the most 
difficult task in the research; however, pullover theory was derived 
successfully and compared with the Standard Test data and the data 
accumulated from the simulated tests. 

After conducting all of the proposed tests, and deriving the pullover 
theory, a reduction factor was recommended to AISI. Additional 
recommendations included a revised Standard Test that models an actual 
installation and an accurate design method for calculating the pullover 
strength that would replace the current provision given in Section E4.4.2. 



Standard PuU-Over Test 



1 



t 



(jh 




I 



Performance in Building Installation 





1 



Figure 1-1 - Initial Boundary Conditions 



Center Lines For 
1" Hole In Jig 



Test Jig 



12 Ga. C-Channel 




Center Lines 
For 1" Hole In 
Flange 



l/8"Stifrener 



8" X 6" Base 
Plate 



Clamping Detail 



2 -1/4" Bolts -4" Long 



#12 Self Drilling Screw 




1 " Threaded 
Rod 



■• Test Specimen 



Figure 1-2 - Schematic of the Standard Pull-Over Test 



Table 1-1 - Proposed Testing Program for Simulated Tests 



Test 
Series 


Installation 
Type 


Supplier 


Gages 


Steel 
Grade 


Number of Tests 


1 


component 


Pascoe 


24&26 


55 


18 


2 


component 


American 


24&26 


80 


18 


3 


component 


Pascoe 


24&26 


55 


10 


4 


component 


American 


24&26 


80 


10 


5 


component 


Pascoe 


24&26 


55 


14 


6 


component 


American 


24&26 


80 


14 


1 


system 


Pascoe 


24&26 


55 


4 


2 


system 


American 


24&26 


80 


4 


3 


system 


Pascoe 


24&26 


55 


4 


4 


system 


American 


24&26 


80 


4 


5 


system 


Pascoe 


24&26 


55 


4 


6 


system 


American 


24&26 


80 


4 


7 


Other Tests as Directed by Sponsor 



Figure 1-3 - Attachment of Sheet at Interior Support (Concentric Concentric) 



Figure 1-4 - Attachment of Sheet at End Support (Eccentric Condition) 



CHAPTER 2 
TENSILE TESTS 



2.1 General 



The tensile test, an essential part of the research, provides a stress/strain 
relationship for each material specimen (Table 2-1). This data is later used in 
a mathematical model for pullover. The developed theory assumes a bilinear 
stress/strain distribution for each material specimen tested (See Figures 2-1 
and 2-2 for illustrations). 



2.2 Procedure 
Three tensile coupons were constructed for each of the four selected 
material specimens in accordance with the American Society of Testing 
Materials (ASTM) A3 70 recommendations. Each coupon was subjected to 
the tensile test where both load capacities and deformations were measured 
during the loading process by means of a Tensile Test Apparatus. Average 
load capacities and percent of elongations were later recorded as seen in 
Table 2-1. See Figures 2-1 and 2-2 for bilinear stress/strain distributions. 



8 



'^ 40000 

8 30000 

*" 20000 

10000 





0.05 



Pascoe Steel Samples 




0.1 0.15 

Strain (in./in.) 



0.2 



0.25 



-•—26 Gage 
-»— 24Gage 



Figure 2-1 - Stress/Strain Distribution For Pascoe Steel 



American Steel Samples 



0.001 0.002 0.003 0.004 

Strain (in./ln.) 



IZUUUU 


t 

-■ 1 


100000 




80000 


y/^ 


Stress (psi) 


/ 


20000 


/ 


01 


(- 1- — 1 1 1 1 1 



-26 Gage 
-24 Gage 



0.005 0.006 



Figuie 2-2 - Stress/Strain Distribution For American Steel 



Table 2-1 - Tensile Test Results 



10 



Property 


Units 


26 Gage 
Pascoe 


24 Gage 
Pascoe 


26 Gage 
American 


24 Gage 
American 


Th. = 


(in.) 


0.021 


0.0234 


0.018 


0.022 


Pu = 


(lbs.) 


2090 


2040 


925 


1180 


DLu = 


(in.) 


1.2412 


1.2279 


0.01125 


0.011 


Py = 


(lbs.) 


1870 


1775 


857 


1150 


Epsilon y = 


(in./in.) 


0.0021 


0.0017 


0.0033 


0.0036 


Red. W = 


(in.) 


1.3065 


1.3367 


0.483 


0.483 


Red. A = 


(in/) 


0.0274 


0.0312 


0.0087 


0.0106 


Fy = 


(psi) 


59300 


50600 


97400 


106900 


Fu = 


(psi) 


66400 


58000 


105000 


109800 


% A Red. = 


(%) 


12.9 


10.9 


1.23 


1.28 


% Elong. = 


(%) 


24.125 


22.788 


0.564 


0.552 


Epsilon u = 


(in./in.) 


0.24125 


0.22788 


0.00564 


0.00552 



■ ' '- V 



CHAPTERS 
STANDARD PULLOVER TEST 



3.1 General 



The ultimate objective of the research was to predict the performance of a 
throu^-fastened sheet in a metal building by performing the Standard Test 
and applying a reduction factor. The reduction factor was determined from 
the results obtained by both the simulated test and the Standard Test. A 
comparison of the final results from both tests will be discussed later in 
Chapter 7. Since the Standard Test is already in accordance with AISl 
specifications, it was selected as the initial test for the analysis. 



3.2 Procedure 
All panels were cut into small sections, approximately 4.5 inches x 12 
inches. The first data series (Pascoe, Fy = 55 ksi) contained 21 steel samples, 
which are listed on Table 3-1 - an illustration of the apparatus is also shown 
on Figure 1 -2. 



11 



12 

The test was simple. After each sample was placed within the tensile 
testing machine, an ultimate load was recorded along with the respective 
failure mode. 



3.3 Results 

Table 3-9 represents data obtained from the previous research at the 
University of Florida. It shows variations among the data with a calculated 
standard deviation of +/- 254. The calculated mean load capacity for one 
screw fastening 26 gage Dean steel (Fy = 80 ksi) was 1,962 pounds. 

Table 3-1 shows variations among the data with a calculated standard 
deviation of +/- 1 80.8 from the mean. The mean was 1,790.9 pounds. There 
are many possibilities that may explain the variations. For one, the failure 
modes changed at random. This may have been caused by the imperfections 
of the material specimens. However, a more realistic possibility could be the 
presence of an eccentric point load, since it is difficult to generate a perfect, 
ideal concentric load with the apparatus used. 

Despite the minor variations, a measurable value representing the ultimate 
load capacity for one screw was obtained by taking a mean and comparing it 
with the entire data series. This was performed in two ways: first, by 



13 

plotting a best fit curve as seen on Figure 3-1, and secondly, by calculating 
the sorted composita and plotting the standardized nonnal distribution as 
seen on Table 3-2. 

The standardized nonnal distribution describes several characteristics of 
the data series (Figures 3-3, 3-4, 3-7 and 3-8). Initially, it shows the 
percentage of those data points that fall within the first standard deviation and 
those that fall within 1 .96 times the standard deviation. An acceptable data 
series should have at least half the data points within the first standard 
deviation. This was the case with the first data series, since 66.6% of the 
data points fell within that range. Secondly, it shows which data points 
should be rejected from the data series. The area of rejection is considered to 
be 1 .96 times the standard deviation or greater. Table 3-2 shows that only 
one test (15) was greater or equal to 1 .96. Since 21 tests were conducted, 
only 1/21 or 4.76% of the tests were rejected and this is shown on the first 
normal distribution curve. 

This statistical analysis, better known as the Standard Z Test, was applied 
to each data series. A total of four specimen types were analyzed and tested. 
Tables 3-1 through 3-9 display the accumulated data, mean load capacity and 
standard deviation for each specimen tested. A revised mean and standard 



14 

deviation was calculated for each composita that contained at least one data 
point in the areas of rejection. 



15 



Table 3-1 - Standard Test Results For 24 Gage Pascoe Steel (Fy = 55 ksi) 

FASTENER DATA (Cold Form Steel Coupons): 



FROM 
TO: 



8/4/94 
9/2/94 



Supplier: Pascoe 
Fy =55 ksi 



TEST# 


TL. LOAD 


COMMENTS 


PL. TH. 




(lbs.) 




(gage) 


1 


1920 


Pullover 


24 


2 


1650 


Pullover 


24 


3 


1800 


Pullover 


24 


4 


1750 


Pullover 


24 


5 


2110 


Pullover 


24 


6 


1720 


Pullover * 


24 


7 


2040 


Pullover 


24 


8 


1590 


Pullover * 


24 


9 


1930 


Pullover 


24 


10 


1870 


Pullover 


24 


11 


1920 


Pullover 


24 


12 


1550 


Pullover * 


24 


13 


1800 


Pullover * 


24 


14 


1720 


Pullover * 


24 


15 


1430 


Disregard-Misfire w/ screw gun. * 


24 


16 


1510 


Pullover * 


24 


17 


2080 


Pullover 


24 


18 


1860 


Pullover * 


24 


19 


1740 


Pullover * 


24 


20 


1820 


Pullover * 


24 


21 


1800 


Pullover * 


24 



* Eccentric Loading 

Mean= 1790.952 

Standard Deviation = 180.8288 

Revised Mean = 1809 

Revised Standard Deviation = 164.9848 



16 



Table 3-2 - Data Points For Standardized Normal Distribution 
(Pascoe 24 Gage) 



SORTED 


SORTED 


TEST# 


CMPSTA 


LOADS 




-1.9961 


1430 


15 


-1.55369 


1510 


16 


-1.33249 


1550 


12 


-1.11129 


1590 


8 


-0.77948 


1650 


2 


-0.39237 


1720 


6 


-0.39237 


1720 


14 


-0.28177 


1740 


19 


-0.22647 


1750 


4 


0.050034 


1800 


3 


0.050034 


1800 


13 


0.050034 


1800 


21 


0.160636 


1820 


20 


0.38184 


1860 


18 


0.437141 


1870 


10 


0.713645 


1920 


1 


0.713645 


1920 


11 


0.768946 


1930 


9 


1.377257 


2040 


7 


1.59846 


2080 


17 


1 .764363 


2110 


5 



2500 T- 



2000 
1790.95 



o 
< 
o 



1500 -■ 



1000 ■■ 



500 



TOTAL LOAD CAPACITY 



♦ ♦ 



10 15 

TEST » 



20 



25 



Figure 3-1 - Best Fit Curve For 24 Gage Pascoe Steel (Fy = 55 ksi) 



T.;« 



17 



Table 3-3 - Standard Test Results For 26 Gage Pascoe Steel (Fy = 55 ksi) 

FASTENER DATA (Cold Form Steel Coupons): 



FROM : 2/27/95 
TO : 2/27/95 



Supplier: Pascoe 
Fy = 55 ksl 



TEST# 


TL. LOAD 


COMMENTS 


PI. Th. 




(lbs.) 




(gage) 


1 


1520 


Pullover 


26 


2 


1820 


Pullover 


26 


3 


1700 


Pullover 


26 


4 


1830 


Pullover 


26 


5 


1620 


Pullover 


26 


6 


1580 


Pullover* 


26 


7 


1670 


Pullover 


26 


8 


1690 


Pullover 


26 


9 


1360 


Pullover * 


26 


10 


1810 


Pullover 


26 


11 


1950 


Pullover 


26 


12 


1570 


Pullover 


26 


13 


1450 


Pullover * 


26 


14 


1620 


Pullover 


26 


15 


1880 


Pullover 


26 


16 


1400 


Pullover * 


26 



* Eccentric Loading 

Mean = 

Standard deviation = 



1654.375 
173.3193 



18 



Table 3-4 - Data Points For Standardized Normal Distribution 
(Pascoe, 26 Gage) 



SORTED 


SORTED 


TEST# 


CMPSTA 


LOADS 




-1.698454716 


1360 


9 


-1.467666814 


1400 


16 


-1.179181937 


1450 


13 


-0.775303108 


1520 


1 


-0.486818231 


1570 


12 


-0.429121255 


1580 


6 


-0.198333353 


1620 


5 


-0.198333353 


1620 


14 


0.090151524 


1670 


7 


0.205545475 


1690 


8 


0.263242451 


1700 


3 


0.897909181 


1810 


10 


0.955606157 


1820 


2 


1.013303132 


1830 


4 


1.301788009 


1880 


15 


1 .705666838 


1950 


11 



TOTAL LOAD CAPACITY 



1800 
1654.38 


- 


♦ 


♦ 


♦ 


• 

* * 




1600 - 


♦ 








♦ ♦ ♦ ♦ 




1400 


■ 








♦ 




1200 - 

g 1000- 

_i 

800 














600 














400 


■ 












200 

























-1 1 — 1 


) . 



10 15 

TEST# 



20 



25 



Figure 3-2 - Best Fit Curve For 26 Gage Pascoe Steel (Fy = 55 ksi) 



19 



Percent of Ciunnlative 
Probability 




Area of Rejection 



Figure 3-3 - Standardized Normal Distribution For 24 Gage Pascoe Steel 



Percent of Cumulative 
Probability 




Area of Rejection 



Figure 3-4 - Standardized Normal Distribution For 26 Gage Pascoe Steel 



20 



Table 3-5 - Standard Test Results For 24 Gage American Steel (Fy = 80 ksi) 

FASTENER DATA (Cold Form Steel Coupons): 
FROM : 2/22/95 
TO : 2/22/95 



Supplier: American 
Fy = 80 ksi 



TEST# 


TL. LOAD 


COMMENTS 


PI. Th. 




(lbs.) 




(gage) 


1 


2150 


Pullover * 


24 


2 


2160 


Pullover * 


24 


3 


2290 


Pullover * 


24 


4 


2010 


Pullover 


24 


5 


2030 


Pullover 


24 


6 


2220 


Pullover 


24 


7 


2190 


Pullover 


24 


8 


2190 


Pullover 


24 


9 


2020 


Pullover * 


24 


10 


1970 


Pullover 


24 



* Eccentric Loading 

Mean = 

Standard deviation - 



2123 
107.3985 



21 



Table 3-6 - Data Points For Standardized Normal Distribution 
(American, 24 Gage) 



SORTED 


SORTED 


TEST# 


CMPSTA 


LOADS 




-1.4246 


1970 


10 


-1.05216 


2010 


4 


-0.95904 


2020 


9 


-0.86593 


2030 


5 


0.2514 


2150 


1 


0.344511 


2160 


2 


0.623845 


2190 


7 


0.623845 


2190 


8 


0.903178 


2220 


6 


1 .554956 


2290 


3 



TOTAL LOAD CAPACITY 












2123 

2000 - 


-.♦ ♦.. 






♦ ♦ ♦ ♦ 


1500 • 






' 


-J 








1000 1 


" 






500 








n 








5 10 15 


20 


25 


TEST# 







Figure 3-5 - Best Fit Curve For 24 Gage American Steel (Fy = 80 ksi) 



22 



Table 3-7 - Standard Test Results For 26 Gage American Steel (Fy = 80 ksi) 

FASTENER DATA (Cold Form Steel Coupons): 
FROM : 2/24/95 
TO : 2/24/95 



Supplier: American 
Fy = 80 ksi 



TEST* 


TL. LOAD 


COMMENTS 


PI. Th. 




(lbs.) 




(gage) 


1 


1740 


Pullover 


26 


2 


1530 


Pullover * 


26 


3 


1550 


Pullover 


26 


4 


2070 


Pullover 


26 


5 


1690 


Pullover 


26 


6 


2040 


Pullover 


26 


7 


1630 


Pullover * 


26 


8 


1610 


Pullover * 


26 


9 


1770 


Pullover 


26 


10 


1650 


Pullover 


26 


11 


1530 


Pullover 


26 


12 


1600 


Pullover * 


26 


13 


1560 


Pullover * 


26 


14 


1690 


Pullover * 


26 


15 


1580 


Pullover 


26 



* Eccentric Loading 

Mean = 1682.667 

Standard Deviation = 167.8633 

Revised Mean = 1625.385 

Revised Standard Deviation = 78.5934 



23 



Table 3-8 - Data Points For Standardized Normal Distribution 
(American, 26 Gage) 



SORTED 


SORTED 


TEST# 


COMPOSITA 


LOADS 




-0.909470061 


1530 


2 


-0.909470061 


1530 


11 


-0.790325511 


1550 


3 


-0.730753237 


1560 


13 


-0.611608687 


1580 


15 


-0.492464138 


1600 


12 


-0.432891863 


1610 


8 


-0.313747314 


1630 


7 


-0.194602764 


1650 


10 


0.043686335 


1690 


5 


0.043686335 


1690 


14 


0.341547708 


1740 


1 


0.520264533 


1770 


9 


2.12871595 


2040 


6 


2.307432775 


2070 


4 



2500 



2000 

1682.67 

1500 

a 

-I 

1000 -I- 



500 



TOTAL LOAD CAPAQTY 



• ♦ 



"♦^^ 



10 15 

TEST# 



— I — 
20 



25 



Figure 3-6 - Best Fit Curve For 26 Gage American Steel (Fy = 80 ksi) 



24 



Percent of Cumulative 
Probability 




Area of Rejection 



Figure 3-7 - Standardized Normal Distribution For 24 Gage American Steel 



Percent of Cumulative 
Probability 




13.3 % 



Area of Rejection 



Figure 3-8 - Standardized Normal Distribution For 26 Gage American Steel 



25 



Table 3-9 - Standard Test Results For 26 Gage Dean Steel (Fy = 80 ksi) 



Test# 


Load 


% Deviation from Mean 




(lb.) 




1 


820 


* 


2 


1740 


11 


3 


950 


* 


4 


1880 


4 


5 


1640 


16 


6 


2250 


14 


7 


1680 


14 


8 


1710 


13 


9 


2170 


10 


10 


1880 


4 


11 


2180 


11 


12 


2330 


19 


13 


2120 


8 



Average = 
STDEV. = 



1962 
254 



Note: * indicates tests that have been omitted from the calculation of the average and 

standard deviation due to errors involved during testing. 



CHAPTER 4 
SIMULATED TESTS 



4.1 Components 
All the initial simulated tests were component tests. These tests included 
multi-fastened systems that contain only one panel for any given test. The 
tests represent the simplest model for typical through-fastened systems. The 
general apparatus for component testing may be seen on Figures 4-1 , 4-2, and 
4-24. 



4.1.1 Concentric Loading 

Concentric loading has been selected as the initial test for the simulated 
testing procedure. This simulates the attachment of a continuous sheet at an 
interior support and is set up to produce perfectly axial tension on the screw 
(Figures 4-1 and 4-2). Eccentric loading was applied later in the research. 

The original apparatus was revised prior to testing. Figure 4-2 illustrates a 
new support condition, which fixes all boundaries associated with the panel. 
This change was necessary since deflections and angle of rotations are zero at 

26 



27 

the supports in an actual building. A fixed boundary also eliminated the 
installation of panel overlaps, which saved set up time and sinqjlified the 
testing procedure. 

Each data series has been divided among suppliers and material type. The 
corresponding data contains three separate data series representing Pascoe, 
American, and Dean suppliers, respectively (Tables 4-1, 4-2 and 4-3). Each 
data series contains a variety of conditions that change during the course of 
the testing. However, note that all Dean steel data was obtained from 
previous research and will not follow the same format. It is important to test 
each panel type in a variety of diverse conditions in order to assess the 
differences between the Standard Test and the simulated building test. 
Therefore, variations of fastener spacing, span length and gage are tested in 
each data series. 

hi order to minimize errors, four tests were performed for each specified 
condition. There are many possible causes for error within this testing 
procedure. They include lining up the screws on the panel, adjusting the 
torque on the screw gun, calibrating the MTS and load cell and fastening the 
panel to the framework. All of these variables are critical to the results. 
Therefore, a mean total load capacity for each specified condition must be 



28 

calculated and later compared with the values obtained from the 
corresponding Standard Test. 

All concentric load tests were conducted with a fixed end boundary 
conditioa Figure 4-2 demonstrates an initial attenpt to model this condition 
using wood braces and C clamps. However, the over-all efi'ect of the custom 
brace was questionable, since it did not provide total resistance to lateral, in- 
plane displacements, hi fact, the brace relied on friction alone to resist lateral 
movement in the panel. There were some indications of lateral movement 
during testing and thus, a variation of the same test was conducted for each 
panel type. This variation included the addition of self-drilling screws 
centered at each valley and placed along the perimeter of the panel (Figure 
4-13). This variation, called the Fixed End Concentric Load Test, insured 
lateral resistance, which decreased the total load capacity of each screw 
tested. Like both the Concentric Load Tests and the Eccentric Load Tests, 
this data was later used to determine the reduction factor for the Standard 
Test (Table 4-8). 



29 

4.1.2 Eccentric Loading 

There are two ways to generate an eccentric load. The first method can be 
achieved by offsetting the screws (Figure 4-3). The second method can be 
achieved by offsetting the supports of the panel (Figure 4-4). In order to 
determine the governing condition, data was obtained from both methods. 
Data for each condition can be seen on Tables 4-4 throu^ 4-7. 

All fastener load capacities obtained from the Eccentric Loading Tests 
were of lesser magnitude than those load capacities recorded from the 
Concentric Tests. This was expected since concentric loads produce 
perfectly axial tension on the screw and represent the most ideal of 
conditions. Like the Concentric Tests, each data series has been divided 
among suppliers and material type. A variety of span lengths and span offsets 
were tested for both eccentric conditions (see Figures 4-5 through 4-12). The 
lowest recorded load capacities were later used to determine the reduction 
factor. Those values are identified, in bold, in Tables 4-4 through 4-7. 

4.1 .3 Revised Apparatus (Load Cell Development) 

New load cells were constructed specifically for the simulated testing 
apparatus and replaced the previous load cell. The original apparatus called 



30 

for only one load cell that rests directly between the two fasteners as seen in 
Figure 4-14. This set up was sufficient, provided that the total load was 
assumed to be equally distributed among the two fasteners present. However, 
when LVDT's were attached to the individual fasteners, tests showed that 
this assumption was not completely accurate. Even under the most carefully 
installed conditions, slight differences of load occurred between the two 
fasteners and in most cases, one fastener failed before the other. 

The problem became a major concern and thus a revised set up was 
necessary. In order to accurately record the precise ultimate load capacity for 
one screw in a multi-fastener system, there must be a load cell placed under 
each and every screw as seen in Figure 4-15. 

All load cells were constructed out of 2024-T4 aluminum and contain four 
strain gauges per cell (two vertical and two horizontal). Dimensions and a 
circuit diagram are illustrated in Figures 4-16 and 4-17. Performance of the 
revised load cells in a multi-fastener system is illustrated in Figure 4-18. 

Lastly, each cell was calibrated. Table 4-9 shows a regression output for 
each cell. Note the R-squared value. The closer to unity, the better the 
response. Each cell reads up to 1,200 pounds of load. 



31 



4.1 .4 The Strain Gage Test 

In order to understand the effects of pullover, it is necessary to understand 
the in-plane stresses and strains that develop within a panel that resists 
pullover. The purpose of the stain gage test was to provide geometric profiles 
and strain contours of a panel resisting pullover. TTie only other way to 
accomplish this is to generate a finite element model of the system. An 
extensive study was made prior to testing and it was determined that a finite 
element model would not be helpful in determining these contours. Due to 
the non-linearities of the system, theoretical modeling would be complex in 
nature and very time consuming. A relatively fast and efficient method for 
determining stress, strain contours was essential, particularly when an infinite 
variety of panel configurations exist for throu^-fastened systems. 
Specifically, such non-linearities include: 

1.) the geometric non-linearifies which primarily pertain to those stiffeners 
within the panel which, in time, lose their effectiveness as the out-of-plain 
load progresses. As a result, this constantly changes the panel's moment of 
inertia. 



32 

2.) the elastic non-linearities, since pullover typically occurs within a highly 
concentrated area that stresses well beyond the linearly elastic limit (i.e. the 
yield point). Depending on the steel grade, such non-linearities may vary. 

A 24 gage, 55 ksi steel panel was selected for the strain gage test. Figure 
4-19 illustrates the strain gage configuration used. Since the highest 
concentration of stresses existed along the center valley of the panel, all of the 
gages were strategically placed in that area, hi addition to the 2 load cells 
that were placed underneath each screw, a total of 12 strain gages, capable of 
measuring up to 10,000 fie, were used. No strain gage was ever placed 
closer than 2 inches from either screw for fear that elongation would surpass 
the 10,000 ^8 limit. This was unfortunate, since it was later determined that 
no gage ever exceeded the linear elastic limit. This proved that the pullover 
area within the panel was very small and highly concentrated. 

Since the dawn of the research, the strain gage test proved to be one of the 
most valuable tests ever performed (Figures 4-25 and 4-26). For the very first 
time a three dimensional view of the system was provided. Panel 
deformations were generated at key phases which are displayed in Figures 4- 
20 through 4-23. Table 4-10 shows the recorded data that generated both the 
strain contours and the panel deformations (Figures 4-20 through 4-23, 4-27, 



\ / " 



33 

and 4-28). Like the component tests described eariier, a concentrated load 
was applied directly to the purlin by means of a come-along (Figure 4-24). 
Each strain value was recorded after one crank on the come-along. 
Successive recordings followed in an identical manner until failure. 

One of the most astonishing observations made was the abrupt change in 
buckling modes from Figures 4-22 to 4-23. It was clear that the web stiffener 
buckling behavior propagated through the valley area, and thus, disrupted the 
continuity of the in-plane tensile stresses that existed within the valley. This 
seems to indicate that the tensile stresses responsible for pullover are highly 
concentrated and exist within a very small area around the screw. The 
remaining in-plane stresses are very low in magnitude and virtually 
insignificant by comparison. It is important to consider that a panel may 
experience several buckling modes within a single load cycle. This depends 
on the effective length and the amount of compressive stress it resists. 

This test proved that the pullover strength of a panel is not effected by 
bending, and thus, such variables relative to bending can be neglected. This 
was a break-through discovery, because it greatly simplified the pullover 
problem. The search for a theoretical model that accurately predicted the 
pullover strength of a panel was now closer than ever before. 



34 

4.2 Systems 
System tests include multi-fastener systems that contain more than one 
panel for any given test. These tests are ideal for modeling through-fastened 
installations and they provide the most accurate data for pullover. The 
general apparatus used for component testing was replaced with the vacuum 
box apparatus, which provided the most useful data for pullover (Figures 4-29 
through 4-31, 4-35, 4-37, and 4-39 through 4-42). 



4.2.1 Introduction To The Vacuum Box Test 

hi order to accurately simulate the effects of a screwed-down metal roof 
subjected to a given wind load, both the supports and loading conditions must 
be duplicated in a lab. In nature, the loading condition is random, distributed, 
and time dependent. One way to simulate this is to construct an isolated 
chamber that becomes the environment. Vacuum boxes are ideal for 
simulating wind loads and are currently being used to test wind resistance on 
glass doors, windows, and other cladding. In fact, several South Florida 
counties have recently mandated vacuum box testing for specific building 
components and there are testing facilities that cater to manufacturers who 
need the testing performed. Figure 4-29 illustrates a typical vacuum box 



35 

assembly. The apparatus is quite simple; however, the solenoid, which shuts 
the incoming air on and off, is itself air actuated. This requires an extra 
supply of air (or a holding tank), which delivers constant air pressure to the 
solenoid. An electrical switch box controlled by a CPU regulates the supply 
of air. 

For the purpose of the simulated pullover test, which is a static load test, 
the assembly can be simplified by removing the solenoid, the holding tank, 
and the electrical switch box. This revised set-up is illustrated in Figure 4-30. 

4.2.2 Apparatus Design And Construction 

The size of the vacuum box greatly depends on the size of the roofing 
system. Standard spacing of purlins is typically 5 feet and initially, a single 
span system was used with one foot of overiiang per side of purlin. An 
additional 4 inches of length insured proper fitting when placing the assembly 
inside the chamber. This established a box length of 7 feet 4 inches. 
Typically, a standard sheet width is 3 feet. An ideal model would provide a 
seam (due to panel overlapping) in the middle of the chamber. With a few 
extra inches to spare for fitting, a gross chamber width of 6 feet 7 inches was 
established (Figure 4-3 1 illustrates the vacuum box detail). 



36 



Prior to constructing the vacuum box, a vacuum pump was selected for the 
test. Previous tests showed that a single 5/8 inch diameter screw attached to 
a 24 gage, grade E steel sheet, resisted a maximum load of 1500 pounds. The 
overall surface area of the roofing system was 42 square feet. Each valley 
within the roofing system required one screw and panel configurations 
included 3 valleys. Therefore, 12 screws were required to fasten a single 
span roofing system. From this information, it was determined that 
approximately 430 psf (3 psi) of negative pressure would be necessary to 
generate a failure. A factor of safety of at least 1 .5 was included prior to 
selecting a vacuum pump. This accounted for the loss of pump efficiency 
with respect to time and the potential for leaks which were inevitable. A 
vacuum punp with a maximum pressure of -5 psi and a volume rate of 1 1 7 
cfm was selected. With a chamber volume of 70 cubic feet, a failure was 
expected within the first minute of activation provided that leaks were kept to 
a minimum. 

The vacuum box was constructed entirely out of wood. Silicon was used 
for caulking material which was critical since the chamber required an air 
tight seal. Wood glue and dry wall screws insured proper connections. Each 



YT f «< 



37 

side wall, standing 20 inches tall, was vulnerable to high pressures caused by 
the internal vacuum (approximately 3 psi). Therefore, whalers were required 
to increase the structural integrity of each wall. The side wall was designed 
to 1991 National Design Specifications for Wood Construction and is shown 
in Figure 4-32. In order to determine the amount of screws necessary for the 
design, calculations of the fastener shear and tensile load capacities were 
included (Figure 4-33). 



4.2.3 Test Methods And Data 

The initial test setup included the simplest representation of an actual 
throu^-fastened metal roof system: the single span system, which contained 
2 supports, 2 panels, and 1 2 fasteners. It was derived from a typical three 
span system shown in Figure 4-34. The figure illustrates a three span metal 
roof system subjected to a specified wind load. The center span, which 
contains the maximum shear stresses and moments within the structure, was 
considered the key model for the initial test. The moment diagram indicates 
the key locations of the inflection points, which are located 1 foot away from 
each interior support. This is how the 7 foot box length was determined 
because, as noted earlier, standard spacing of purlins is typically 5 feet. 



38 



The first vacuum box test was constructed in this manner, but there were 
several difficulties (Figure 4-35). Firstly, due to the inflection points, the 
system was limited to 7 feet. At this specified length, where a 1 foot 
cantilever existed on each side of the supports, a significant amount of shear 
existed at each free end of the system (Figure 4-36). This shear was difficult 
to model in the lab. Secondly, the 5 foot span appeared quite large when 
placed within the small isolated chamber. Without the ability to apply shear 
at the fiiee ends, the panels were susceptible to buckling. Thirdly, the absence 
of lateral braces caused both supports to roll, which, in addition to the span 
length, contributed to the massive buckling behavior of both panels (Figure 4- 
37). 

Due to all of these difficulties, the first test never generated a pullover 
failure and a number of revisions were implemented. The second test was a 
tremendous improvement. In order to minimize panel buckling, it was 
determined that the maximum positive moment, generated at mid-span, must 
equal the maximum negative moments, generated at the supports. Figure 4- 
38 shows the calculation for the span length which creates this condition. It 
was determined that a span length of 4. 1 feet was sufficient. Figures 4-39 



39 

and 4-40 illustrate the revised test setup. Note the addition of lateral braces 
for both supports which eliminated the rolling action previously observed. 

The revisions made on the single span system (Test 2) proved to be 
satisfactory; however, the test required far more load cells than could be 
provided (at least 8 at all times) and it was difficult to control the buckling of 
the panels. Since the 5 foot standard span length was already reduced to 4. 1 
feet, it was decided that a two span system replace the existing single span 
system (Figure 4-41). This system reduced the span length to 3.5 feet. Panel 
buckling was no longer critical and the system required only six load cells for 
any given test. This reduced setup time and greatly simplified the testing 
procedure. Failures were generated along the center support where shear and 
moment were both at a maximum (Figure 4-42). A theoretical model is 
currently shown in Figures 4-43 and 4-44. 

Deflections were recorded for each test. This data was necessary for 
load-deflection curves and validating the theoretical data provided in Chapter 
5. Deflection calculations for each system are provided in Figure 4-45. 

No static load test ever produced better pullover data than the vacuum box 
test. For the first time, subsequent pullover failures were observed in a 
through-fastened metal system Each screw within the system was monitored 



40 

independently. The pre-tensioning effects were recorded and the load 
capacities were logged within quarter second intervals. 

Typically, the initial pullover failures were concentric followed by two 
distinct eccentric failures. The initial eccentric failures resulted from the 
biaxial tensile stresses developed within the steel panel. This biaxial stressed 
condition provided the lowest load capacities. Conversely, the hi^est load 
capacities were generated from the secondary eccentric failures which 
occurred at the free edges of the system. These locations developed uniaxial 
in-plane stresses within the panel and consequently did not provide the typical 
reduced pullover strength observed earlier in the component tests. 

The grade E steel did provide slightly higher load capacities than the lesser 
grade material. However, it did not provide a significant increase in pullover 
strength because its brittle nature produces lower displacements and lower 
deflection angles. Unfortunately, higji strength steels do not always 
contribute to pullover strength and in some cases, depending on the specific 
conditions, may even reduce the pullover strength of a through-fastened 
system. Chapter 5 explains in detail how steel strength affects pullover 
strength. See Tables 4-1 1 through 4-13 for pressure box data. 



41 







1 , \^ 


t 





Figure 4-1 - Original Apparatus For Simulated Test 



42 






Figure 4-2 - Revised Apparatus For Simulated Test With Typical Panel 
Deformations 



Table 4-1 - Simulated Test Results For Pascoe Steel (Concentric) 



43 



FASTENER DATA (Concentric Loading) ; 

Supplier : Pascoe 

Fy= S5ksi 

From : 6A8/94 

To : 7/8/94 



F - 1 screw placed at center of 
each outer valley. 

C - 2 screws placed in center valley. 



TEST# 


SPACING 


SPAN 


TL. LOAD 


LD./SCW. 


COMMENTS 


TH. 






(in.) 


(lbs.) 


(Ibs./scw.) 




(gage) 


1 


F 


17 


1700 


re^n 


Uneven pullover. One side 
buckled but no pullover. 


24 


2 





17 


1150 


575 


The entire panel buckled. 
Pullover never occurred. 


24 


3 


C 


17 


i.Ton 


650 


The entire panel buckled. 
Pullover never occurred. 


24 


4 


F 


17 


2250 


1125 


Uneven pullover. One side 
buckled but no pullover. 


24 


5 


F 


17 


2400 


1200 


Uneven pullover. One side 
buckled but no pullover. 


24 


6 


C 


13 


2150 


1075 


Even pullover. Massive plate 
buckling. 


24 


7 


C 


13 


1960 


980 


Even pullover. Massive plate 
buckling. 


24 


8 


F 


17 


2300 


1150 


Even pullover. Massive plate 
buckling. 


24 


9 


F 


17 


2200 


1100 


Uneven pullover. No buckling. 
Failure at both points. 


26 


10 


F 


17 


2200 


1100 


Uneven pullover. No buckling 
Failure at both points 


26 


11 





17 


2000 


lonn 


Even pullover. Massive plate 
buckling. 


26 


12 


C 


17 


2150 


1075 


Even pullover. Massive plate 
buckling. 


26 


13 


F 


17 


iqfin 


975 


Uneven pullover. No buckling. 
Failure at both points 


26 


14 





17 


2100 


1060 


Even pullover Massive plate 
buckling. 


26 


34 





13 


2400 


1200 


Even pullover Massive plate 
buckling. 


24 


35 





13 


?nnn 


1000 


Even pullover. Massive plate 
buckling. 


24 


36 


F 


17 


2100 


infin 


Uneven pullover. No buckling. 
Failure at both points. 


26 


37 





17 


2000 


innn 


Even pullover Massive plate 
buckling. 


26 



Table 4-2 - Simulated Test Results For American Steel (Concentric) 



44 



FASTENER DATA (Concentric Loading) : 

Supplier : American 

Fy - 80 kt\ 

From : 11M/94 

To : 12/1/94 



F - 1 screw placed at center of 
each outer valley. 

C - 2 screws placed in center valley. 



TEST# 


SPACING 


SPAN 


TL. LOAD 


LD./SCW. 


COMMENTS 


TH. 






(In.) 


lbs.) 


(Ibs./scw.) 




(gage) 


15 




21 


1200 


600 


Minor plate buckling. 
Uneven pullover. 


26 


16 




21 


2000 


1000 


Minor plate buckling. 
Uneven pullover. 


26 


17 




21 


ipon 


VO 


Minor plate buckling. 
Uneven pullover. 


26 


18 




21 


2000 


1000 


Minor plate buckling. 
Uneven pullover. 


26 


19 




21 


2100 


1050 


Minor plate buckling. 
Uneven pullover. 


26 


20&21 


C 


21 &17 


Apx. isnn 


Apx 750 


Massive plate buckling 
No failure No pullover. 


26 


22 


c 


13 


2000 


inoo 


Massive plate buckling 
Even pullover. 


26 


23 





13 


2300 


1150 


Massive plate buckling. 
Even pullover. 


26 


24 


c 


13 


1900 


950 


Massive plate buckling. 
Even pullover 


26 


25 


c 


13 


2500 


1250 


Moderate plate buckling. 
Even pullover 


24 


26 


c 


13 


2400 


1200 


Moderate plate buckling. 
Even pullover. 


24 


27 


c 


13 


2400 


1200 


Moderate plate buckling 
Even pullover. 


24 


28 


c 


13 


2100 


infiO 


Moderate plate buckling. 
Even pullover 


24 


29 




13 


2200 


1100 


Minor plate buckling. 
Uneven pullover. 


24 


30 




13 


1700 


850 


Poor Test Results. 


24 


31 




13 


2480 


1240 


Minor plate buckling. 
Uneven pullover. 


24 


32 




13 


2460 


1230 


Minor plate buckling. 
Uneven pullover. 


24 


33 




13 


2500 


1250 


Minor plate buckling. 
Uneven pullover 


24 



Table 4-3 - Simulated Test Results For Dean Steel (Concentric) 



45 



Test No. 


Total Load 


Load / Screw 
(lbs.) 


% Deviation 
From Mean 


Deflection Of 

Left Fastener 

(in.) 


Deflection Of 

Right Fastener 

(in.) 


Load Rate 
(IbsJSec.) 
















A 


1553 


777 


* 


• 


* 


• 


B 


1400 


700 


* 


* 


• 


• 


C 


1350 


675 


• 


• 


• 


• 


1 


1599 


800 


2 


0976 


0.976 


178 


2 


1773 


887 


11 


1.201 


1.422 


17.2 


3 


1686 


843 


7 


0.987 


0.970 


24.8 


4 


1241 


620 


26 


0.774 


0.773 


86 


5 


1637 


819 


4 


0.926 


0.931 


12.6 


6 


1617 


809 


3 


0.965 


0.933 


11.6 


7 


1652 


826 


5 


0.956 


0.876 


14.9 


8 


1462 


731 


8 


0.887 


0.883 


77 


9 


1501 


751 


5 


0.870 


0.887 


8.8 


10 


1521 


761 


3 


0.937 


0.906 


84.5 


11 


1515 


757 


3 


0.972 


0.918 


7.3 
















Average = 


1569 


782 










STDEV. = 


148 


70 

























NOTES : 

1) * indicates tests that have been omitted from the calculation of the average and 

standard deviation due to errors involved during testing. 



2) 



Deflections that are underlined represent the fastener that failed. 



46 



1 I — I ^ 



Figure 4-3 - Offsetting The Screws 




Figure 4-4 - Offsetting The Panel Supports 



47 



Table 4-4 - Simulated Test Results (Eccentric Loading) For Pascoe Steel 

FASTENER DATA (Eccentric Loading) : 
(Condition #1 - Offsetting The Screws) 



Supplier : 


Pascoe 


Fy = 


55ksi 


From : 


4/3/95 


To: 


4/26/95 



TEST 
NUIVIBER 


SPACING 
FROIVI CL 


SPAN 
LENGTH 


TOTAL 
LOAD 


PANEL 
THICKNESS 














(in.) 


(in.) 


(lbs.) 


(gage) 












1 


2 


13 


923 


24 


2 


3 


13 


972 


24 


3 


9 


13 


818 


24 


4 


10 


13 


678 


24 


5 


12 


13 


850 


24 


6 


2 


13 


952 


26 


7 


3 


13 


799 


26 


8 


9 


13 


905 


26 


9 


10 


13 


860 


26 


10 


12 


13 


729 


26 



,f»p- 



48 



a 
n 
U 



1000 -, 

900 - 
800 
700 -- 
600 ■ 
500 - 
400 - 
300 
200 
100 + 





^ \ 



2 4 6 8 10 

Distance From Fastener To Center Load (in.) 



12 



Figure 4-5 - Eccentric Loading Condition 1 For 24 Gage Pascoe Steel 




Figure 4-6 - Eccentric Loading Condition 1 For 26 Gage Pascoe Steel 



49 



Table 4-5 - Simulated Test Results (Eccentric Loading) For American Steel 

FASTENER DATA (Eccentric Loading) : 
(Condition #1 - Offsetting The Screws) 

Supplier : American 

Fy = 80 ksi 

From : 5/1/95 

To : 5/19/95 



TEST 
NUMBER 


SPACING 
FROM CL 


SPAN 
LENGTH 


TOTAL 
LOAD 


. PANEL 
THICKNESS 














(in.) 


(in.) 


(lbs.) 


(gage) 












1 


2 


13 


507 


24 


2 


3 


13 


530 


24 


3 


9 


13 


385 


24 


4 


10 


13 


701 


24 


5 


12 


13 


660 


24 


6 


2 


13 


535 


26 


7 


3 


13 


605 


26 


8 


9 


13 


290 


26 


9 


10 


13 


356 


26 


10 


12 


13 


347 


26 



50 

















800 - 
700 ^ 


1 — 




_,_ 


_ .- 




600 - 






/ 




n 








1 




^ 


500 - 


. 


* — "''*~~ — ~~-— _ 


/ 




s. 

(a 






~~~^ — ^^___ 


/ 




O 

■a 
n 
O 

_l 

«> 
c 

n 
u. 


400 - 
300 - 

200 
100 


■ 




~~~ ^ 




y 


"^■^ 








i 

J 

c 


r 










2 4 6 


8 10 


12 






Distance From Fastener To 


Ce nte r Load (in.) 





Figure 4-7 - Eccentric Loading Condition 1 For 24 Gage American Steel 



700 



600 -- 



500 



S 400 - 

u 

8 30G 



200 



100 



{ 




2 4 6 8 10 

Distance From Fastener To Center Load (in.) 



12 



Figure 4-8 - Eccentric Loading Condition 1 For 26 Gage American Steel 



51 



Table 4-6 - Simulated Test Results (Eccentric Loading Condition 2) For 
Pascoe Steel 

FASTENER DATA (Eccentric Loading) : 
(Condition #2 - Offsetting The Supports) 



Supplier : 


Pascoe 


Fy = 


55ksi 


From : 


5/1/95 


To: 


6/18/95 



TEST 
NUMBER 


ACTUAL 
DISTANCE 


SPAN 
LENGTH 


PEAK LOAD 


PANEL 
THICKNESS 








MAX. 


MIN. 




(#) 


(in.) 


(in.) 


(lbs.) 


(lbs.) 


(gage) 














1 


13.5 


15 


813 


567 

* 


24 


2 


11.5 


13 


730 

* 


461 


24 


3 


9.5 


11 


663 

* 


541 


24 


4 


7.5 


9 


925 


583 

* 


24 


5 


5.5 


7 


863 

* 


473 


24 


6 


3.5 


5 


847 


608 

* 


24 


7 


23.5 


25 


800 

* 


415 


24 


1 


13.5 


15 


628 


596 

* 


26 


2 


11.5 


13 


762 


610 

* 


26 


3 


9.5 


11 


562 

* 


532 


26 


4 


7.5 


9 


495 


425 

* 


26 


5 


5.5 


7 


785 

* 


683 


26 


6 


3.5 


5 


755 

* 


555 


26 


7 


23.5 


25 


754 

* 


522 


26 



* Indicates Fastener Failure 



52 





1000 J 




900 


I 


800 
700 - 


(0 
Q. 

5 

T3 

ra 
o 

_i 


600 
500 - 
400 - 


c 

s 

M 


300 - 
200 




100 - 
- 




5 10 15 20 

Distance From Fastener To Fixed Boundary (In.) 



-MAX. 
-MIN. 



25 



Figure 4-9 - Eccentric Loading Condition 2 For 24 Gage Pascoe Steel 



800 



700 



S 600 





500 


a. 
a 
O 
■a 

(0 


400 


-1 


300 


0) 




01 


200 



100 




5 10 15 20 

Distance From Fastener To Fixed Boundary (in.) 



25 



-MAX. 
-MIN. 



Figure 4-10 - Eccentric Loading Condition 2 For 26 Gage Pascoe Steel 



53 



Table 4-7 - Simulated Test Results (Eccentric Loading Condition 2) For 
American Steel 

FASTENER DATA (Eccentric Loading) : 
(Condition #2 - Offsetting The Supports) 



Supplier : 


American 


Fy = 


SOksi 


From : 


5/1/95 


To: 


5/19/95 



TEST 
NUMBER 


ACTUAL 
DISTANCE 


SPAN 
LENGTH 


PEAK LOAD 


PANEL 
THICKNESS 








MAX. 


MIN. 






(in.) 


(in.) 


(lbs.) 


(lbs.) 


(gage) 














1 


13.5 


15 


950 


867 

* 


24 


2 


11.5 


13 


888 


740 

* 


24 


3 


9.5 


11 


1001 

* 


859 


24 


4 


7.5 


9 


1065 

* 


828 


24 


5 


5.5 


7 


959 

* 


822 


24 


6 


3.5 


5 


708 

* 


499 


24 


7 


23.5 


25 


984 

* 


855 


24 


1 


13.5 


15 


451 

* 


414 


26 


2 


11.5 


13 


638 

* 


560 


26 


3 


9.5 


11 


341 

* 


289 


26 


4 


7.5 


9 


413 

* 


346 


26 


5 


5.5 


7 


563 

* 


519 


26 


6 


3.5 


5 


485 

* 


285 


26 


7 


23.5 


25 


660 

* 


480 


26 



* Indicates Fastener Failure 



54 





1000 - 


1 
I 


yP \k_— ■-^* i 








>i 




u 


800 


/ / >s^ ^ 




V*^ / Til 1 


a 






Q 




/ ■ ■ ' ■ ' 1 


o 


600 ' 


/ 1 






/ I 






J 






■ 








^ 


400 




C 






4> 


















£ 


200 



1 

h— — ^ 1 1 1 1 



-•—MAX. 
-«— MIN. 



5 10 15 20 

Distance From Fastener To Fixed Boundary (in.) 



25 



Figure 4-11- Eccentric Loading Condition 2 For 24 Gage American Steel 



700 T- 



- 600 

vt 

n 

5 500 - 

I 400 

g 300 



c 200 



u. 100 




5 10 IS 20 

Distance From Fastener To Fixed Boundary (in.) 



-MAX. 
-MIN. 



— I 
25 



Figuie 4-12 - Eccentric Loading Condition 2 For 26 Gage American Steel 



Table 4-8 - Fixed End Concentric Load Test Data 



55 



FASTENER DATA (Concentric Loading / Edges Fastened) : 



From 
To: 



6/8/95 
6/17/95 



COMPANY 


SPACING 


SPAN 


PEAK LOAD 


PANEL 


Fy 






MAX. 


MIN. 


THICKNESS 






(in.) 


(lbs.) 


(lbs.) 


(gage) 














Pascoe 
55 ksi 





13 


560 


504 


24 














Pascoe 
55 ksi 


C 


13 


413 


281 


26 














American 
80 ksi 


c 


13 


644 


570 


24 














American 
80 ksi 


c 


13 


515 


466 


26 















Note: All Screws Failed Simultaneously. 



^ 



One Screw Per Valley 



Screws Tested 



Edge Stiflfeners Were Clamped 



Figure 4-13 - Fixed End Concentric Load Test (Panel Layout) 



56 



Fastener 



Lead To Data 
Acquisitionor 



1 I — i^r 




Metal Panel 



Purlin 



Threaded Rod 
With Nut 



Load CeU 



Actuator 



Figure 4-14 - Old Apparatus 



Fastener 



Lead To Data 
Acquisitionor 




I — I r 



l}a 



Load Cell 




Metal Panel 



Purlin 



Threaded Rod 
With Nut 



Actuator 



Figure 4-15 - New Apparatus 



57 



2024-T4 Aluminum 



Solder Pads 



Vertical 
Strain Gage 




Horizontal 
Strain Gage 



Figure 4-16 - New Load Cell 



White Lead 
(+ Readout) 




Solder Pad 



Red Lead 
(+ Voltage) 




^ 



Strain Gages 



Black Lead 
(- Voltage) 




Green Lead 
(- Readout) 



Figure 4-17 - Load Cell Circuit 



58 




Figure 4-18 - Revised Load Cells For Multi-Fastener System 



59 



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m 

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CM 

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d 



3 

a. 
^* 

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o 

c 
o 

« I 

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E 

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ai 



w 



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3 
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60 



5.5 in. 
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- 


- — 




— 












18 in. 








18 in. 











12 in. 7 in. 12 in. 

\t tifUift »!«(« 1\ 

2.5 in. 2.5 in. 



10000 HE 

Strain Gage 



Load Cell 2 
Load Cell! 



12 



24 Ga. Pascoe Steel 
(Fy = 55 ksi) 



2 ' i 1 



4 j '3 



'm m 



m m 



\ 



10 



11 > 




19 



2.5 in. 



< — ► 



2.75 ini 2.75 in.l 



-M »4 »« 



2.5 in. 



0.75 in. 1 



6 in. 



3 in. 



3 in. 



2 in. 



2 in. 



2 in. 



■0.75 in. 



Figure 4-19 - Strain Gage Configuration 



61 




190 lbs. 190 lbs. 



Figure 4-20 - Before Web Yields 






571 lbs. 571 lbs. 



-7000 



571 lbs. 571 lbs. 



-7000 



Figure 4-21 - After Web Yields 



62 




532 lbs. 532 lbs. 



Figure 4-22 - After Web Buckling 



532 lbs. 532 lbs. 




677 lbs. 677 lbs. 



677 lbs. 677 lbs. 



Figure 4-23 - Ultimate Strain 



63 




y- %r 



, I 



Figure 4-24 - Apparatus For Strain Gage Test 



64 




Figure 4-25 - Strain Gage Test Includes 2 Load Cells And 12 Strain Gages 




Figure 4-26 - Computer Used For Strain Gage Test 



65 



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m 

CD 
00 


en 

CO 
CD 

o 

CM 

1 


CO 

oo 

00 

m 

1 


CM 
U3 

iri 
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1 


00 

in 

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CO 


in 

CM 

CO 
O 


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CO 

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1 




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O 
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1 


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at 

ui 


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CO 
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m 

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cn 

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-6000 -4000 
-8000 -6000 
-10000 -8000 




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68 



Transducer 



CPU 



Flexible Hose 



Solenoid 



Vacuum Box 



^ Manometer 



Airline 



Airline 



Blower 



Switch Box 



Holding Tank 



Figure 4-29 - Standard Vacuum Box Assembly 



Vacuum Box 



Transducer 



C T T T "[ 



CPU 



Vacuum 



O 

Bleeder Valve 



Leads To Load Cells 



Figure 4-30 - Revised Vacuum Box Assembly 



69 



Purlin 



Vacuum Box 



Whaler 



Vacuxmi Pump 



Bleeder Valv 



Brace 




Tarp or Plastic 
Sheathing 



6' - 7" 



Elevated View 



l'-2" 



r-2' 



Seam Due To Panel 
Overlapping 



Purlin 



Brace 



Vacuum Pump — ► 



Bleeder Valve 



Side View 



Plastic Sheathing 




Box 
Perimeter 



r - 8" 



Whalers 



Figure 4-3 1 - Vaccum Box Detail 



70 



Web 



1.5" X 



3 psi 



d ^ 
1.5" 



1 ' - 8" 



Flange 



54 lb/in. 

u wv/v/\ /vy\/\/\ J 




M SM 

S 
3V 3(2268) 2268 



/ <F ' where f = — = far red. sec tion ; 

b b b c 2 

bd 



6(47628) 190512 
F •> > 

b 2 2 

I5d d 



Jb< Fy' where f^ 

2bd 2(l5)d 

^^'=^^(0.9)(1.15) = 1.035F^ 
Fv'=Fy(0.9)(2) = l%Fy 



l^v'^ 



2268 



^b^ 



190512 



2 &Fy> 



2268 



1.035(fi^' ) md) 

Average Southern Pine Has 



Fy = 100 psi &Ff^ =1500 psi 



IFd = 8" F^ = 2876 psi & F^ = 1575 

^ , 6(23814) 1134 
F. > & F '> 

I5d^ d 



psi 



h^ 



190512 



^v^ 



1.03 5(rf) 
1134 



1.8(rf) 



■^F^ >1438/J5/ OK 



-> Fy = 78.75 psi OK 



ll2x%' s of Southern Pine is acceptible 



Figure 4-32 - Web Design (Neglecting Contribution From Flange): 



71 




A36 Steel F = 36fo/ 

V 

1 1 2 2 

— in. Diameter Screw Has A = p( — ) = 0.01227 in. 
8 16 



P = 36(0.01227) = 0.441 kips = [441 lbs. 

F =0.4F =\4.4 ksi 
V y 



— = 14.4 ksi ; emax = ^'max ^ ^f'^re. ^'max = — 
Id 2 

2 3 4 

7rr 4r 4r ur 

Qm^=i-r)(—) = ^-^b = 2r;I = —-- 
2 3;r 6 4 

4r 4r 

V{ ) V{ ) 

6 6 



nr 4r 

— &y = — 

3;r 



4 ~ 5 

Ttr nr 

( )(2r) ( ) 

4 2 



2/-^ 2 



■X 5^- - 2 

J nr inr 



4V 3nr (14.4) 

J - 14.4 ksi ; F„ = = 0.132 kips = 



3nr 



132 /65. 



Figure 4-33 - Fastener Properties 



72 



1200 



V 



M 




., , -6000a: ^,^ 
/Wl=— ^+2400 

J/(x)j ^ = -600a:^ +2400X 



a:(-600x + 2400) = O ) x = 0, 4 



f{x)^ =-1200x + 3000 
if(x)^dx = -600x^ + 3000a: + c 



600x^ 


- 3000x + 


3000 


= 


3000 ±1342 
1200 


= 1.38, 


3.62 



Figure 4-34 - Three Span System (ASD 2-308 & 36) 



73 




Figure 4-35 - The Vacuum Box Used For The Simulated Pullover Test 



74 



2400 lbs. 



12001bs./ft. 



\i\i\i\i\i\i\i\(\jTm 




3000 lbs. 



Existing Shear 
At Free End 




Additional Loads 
Required In Model 



2400 lbs. 



Figure 4-36 - Shear at Free Ends 



75 




Figure 4-37 - Massive Panel Buckling 



76 



M 



./\/\/\J\/\/\/\/\. 




X\ CO 


(l-x) 

2 




(l-x) 

2 


wx 

2 


w(I-x) 




^ 


w{l-x) ^^^^-^^ 
2. H-ZClx - /) 
8 


wx 

2 


^ 


8 8 


^ 



wi{2x-r) w{i-xy 



8 8 

llx-l^ =1^ -2lx + x^ 

x^ -4lx + 2l^ =0or x'-28x + 98 = 
28 ±^28' -4(98) 



x = 4.\ft. or 49.2 m. 



Figure 4-38 - Balancing Positive And Negative Moments 



77 




Figure 4-39 - The Revised Single Span System 




Figure 4-40 - Lateral Braces And Decreased Span Length Minimized Panel 
Buckling 



78 




Figure 4-41 - The Two Span System 




Figure 4-42 - Pullover Failures Occurred At The Center Support 



79 



9o 



.y\/\/v/\/\/v/\/\. 




El 




2 ^ 2 "^ T""'"" 


^0 


R 


V, 



B.C's: H<0) = A/(0) = & h<-) = & h</) = M(/) = 

< X < -: H', (x) - < X < /: Wj (x) 

Unknowns: V^, V,, R, 0^, 0, 





" ' /" " /2^ (>El 24EI 



2£7 6£/ 



H',"W = 



M/"(X) = 



qo^_Vo£ 

2EI n 



/.3 



H'2W = ^0^ 



T^ 3 4 ^(X ) 

V^x q^x ^ 2 



H'/(X) = ^„ 



6£7 24£/ en 



1.2 



+ ■ 



in en 



in 
vx qx' ^(^-() 

H-,"(x) = -?^^ + -^» 2 



m-2"'(a:) = "- + 



n lEi 
K . ^ox R 



n 



n n n 



/, 



/ vj' 



qj' 



2 "2 48£^ 384£/ 



V P at 



/?/^ 



6£/ 24£^ 48£7 



M(/) = -£/h'2"(/) = = -1^ 



-VJ^qJl_Rl_ 
~W 2^ 2X( 



3 Equations & 77/ree Unknows: -V^, 6^, R: 

1 ^ .iVl__?o^ 
" 24£7 192£^ 



6£/ 24£/ 48£/ 

qoJl^Rl 

2 2 



3.r„/-^2^ + — = 



Figure 4-43 - Two Span System (Solved By Method Of Initial Parameters) 



80 



V i^ 
1&2: » 



goi' 



Kr 



qJ\^_Ri' 



24EI \9in en iaei asei 



3Vf RJ' 

■ + ■ 



34£7 48£/ 192EI 



" 192£7V 3/^ J 48£/V 3/' 



192 



& into 3 



56qf Rl Rl qf 



Rl qf 56qf 



192 



& R = 



192 
3^0/ 168^0/ 
2 192 



+ • 
6 2 



/? 



^3 7 



5^0/ 



V2 gy" 8 

56qJ 5qJ ^ 36qJ 
192 



192 48 

i3 



^0 = 



36q,r 



qf 



\2q/ 



\92{24EI) \92EI 460SEI 



Check: 

\ 192 J 



f 12 ^ 

V 



6EIJ 



_gol^j5qf 
24£/ I 8 J 



48£/. 



4608£7 



5v' Inspection. V^ = V, 



36qJ 



Check: 



36qJ 
V\92J 



2 + - 



*'l-- 


192 


8 


q,l OK V 



^ 36qj' 



;3 

^\\52EIJ 24£/ 



+ 



384£^. 



Figure 4-43 — Continued 



81 



y\/\/\j\/\/\/\/\ 



^ 







n. 



M 



1/2 

4 






. 




1/2 A 


0.1875W/ 




0.625w/ 


0.1875W/ 


^1875^/ 




0.3 125^/ 


s..^^^ 






^^^ 


« — 


0. 8125/ 

» 


^"^^\ 


*v 


0.1875/ 
•< » 


0.1875/ 


^ 




0.8125/ 


^^^^^ 






-0.3 125^ 






-0.1875VI' 


0.0 176^/= 




^ 








, 


0.0176w/= 








-0.109 










0.375/ 

4 




»■ 


0.125/ 


0.125/ 






0.375/ 














V____ 




-^ 


K 




^ 




_____^ 











X 

ji-wc+0.W5\ii)dx=0 )[-05vw^ + 0.1875wi!x]^ =0 



x(0A^5wi-05wc) = >x=0, 03751 



Figure 4-44 - Two Span System (Theoretical Model) 



82 



V 



M 




wa. 



V{x)^-EI[-wx + ^=-] 

M(x) = lVix)dx 
M{x) = -EIW{x)" 



Mix) = -EI 



~wx wax wl wla wa^ 

+ + 



W(xy'=-—M(x) :. W(xy^ \Mix)"dx 



EI 

w(xy=-~ 

EI 



-wx^ wax^ ( wl^ wla wa^^ 



■ + ■ 



■+ — 



+ - 



8 ; 



x + c 



w{xy=o@x 



a 



W{x) = \w(,xydx 
W{x) = ^ 



„ -wa^ wl^a wla^ 

= — ■_ + ->rc :. c = 



-^ 



48 16 



8 



wa^ wl^a wla^ 
48 16 



EI 



4 3 /^ 

-wx wax 

+ + - 



24 12 



wP wla wa^^x^ fwa^ wl^a wla^^ 



V 8 



8 J 



■ + - 



48 16 8 ; 



8 



x + c 



fViO) = .-. c = 



JCL ^ 



WX* wax^ 



24 12 



w(l-af 
16 



x'~ 



w{l-aYa wa 

V 16 24 



3^ 



Figure 4-45 - Deflection Calculations 



83 



V{x) = -EI[-wx] 
M(x) = ^V(x)dx 
M(x) = -EIW{x)" 



Mix) = -£/ 



-wx 



■ + c 



lV{x)"= M{x) :. Wixy= \w(x)"dx 

F.I J 



EI 

w{xy=-— 



-H-X 



H-C 



From Previous Calculation: W{xy- 



~E1 



wa' M/fa wla^ 
48 16 8 



@x = 0: 



+ 



48 

w{xy=- 



16 

J_ 
EI 



-w 



l-a 



8 



MX wl wa I 

+ 



+ c -^ c 



wr wa^l 
48 16 



48 16 



W(x) = jW(xy=-^ 



wx 
~2A 



r,..ii 



■ + 



W{x) = 0@,x = \—\:c 



wl' wa^i\ 
VA% 16 

l-a 



x + c 



2 J 



^.../3 



24 



wP wa^t 

48 16 , 



( l-a\ 
\ 1 J 



W{x), ^ - 



EI 



wx 



4 r 



24 



wl' wa^r 
I 48 16 y 



x + 



(l-aV 

w\ 

\ 2 J 

24 



wP wa^r 
V4S 16 y 



2 J 



Figure 4-45 ~ Continued 



The Two Span System (Figure 16): 



' ■m » -' 



84 



r(x) = -M/x + 0.1875H'/ 

Mix) = j V{x)dx = -05wx^ + 0.1 875w/x + c ; M(0) = .-. c 

^J-0.167mx' +0.09375w/x' +c\ 






pr(-)'=o.-. c 

2' 48 



0.0234 vv/' ; c = -0.0026mV' 



W{x) = f fr(x)'a!x = — fo.0417Hx' - 0.03125H'i:x' + 0.0026i 

•' hi l 



^(0) = O .-. c = 



1 



^i^)cL = -rT[0.0417M'x'* -0.031 25m'/x' +0.0026h/'x1 



Figure 4-45 ~ Continued 



85 




Figure 4-46 - The Vacuum Pump And Ball Valve 




Figure 4-47 - The Pressure Transducer 



86 






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— 


mel buckling. Big improvement. One pullout failure was 

ing of the threads may have caused this or perhaps the screw 

previously drilled. Purlins were used for more than 1 test. 




H^t^o-.--q-fcSoo2cMr-cNincocn-.-cMr-orla)^ina)S:^S° 
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CHAPTER 5 
PULLOVER THEORY 



5.1 General 



Pullover, an in-plane tensile failure, is caused by a high concentration of 
tensile stresses which develop within the metal panel and around the fastener. 
These tensile stresses, which may be uniaxial or biaxial, are govemed by the 
boundary conditions. Biaxial tensile stresses are most common in an actual 
installation, because the perimeter of the panel is typically fixed. The only 
exception to this installation may be the placement of small steel roof tiles 
which contain two or more screws in a single row per tile (Figure 5-1 ). This 
would create a uniaxial stressed condition if no more than two fixations 
existed for any given screw within the system. However, this is not a typical 
method of installation and it does not pertain to most througji-fastened metal 
roof and wall systems. 



99 



100 
5.2 Uniaxial Tension 
The AISI specifications, section E4.4.2 is limited to the uniaxial condition 
and cannot be used for the biaxial stressed condition typically identified with 
most systems. This is one of the greatest flaws in the section. The uniaxial 
condition is contributing to the poor, unconservative predictions of pullover 
strength; therefore, it will be necessary to add the biaxial condition to the 
section. This addition will be discussed later and it will include a revised 
standard pullover test that incorporates the biaxial stressed condition. 



5.2. 1 AISI Specifications (Section E4.4.2) 

One major objective was to provide equations that accurately predict the 
pullover strength of a given system; however, it was a priority to thoroughly 
understand the current provisions within the AISI specifications. Section 
E4.4.2 contained one design equation derived from the standard pullover test. 
The derivation was taken directly from the test apparatus. A free body 
diagram is shown in Figure 5-2. For unknown reasons, a reduction factor of 
0.75 was included; thus, reducing the standard equation to: 

P^ = l5t,d^F^, (5 J) 



101 
Note that the present equation neither includes the actual initial support 
condition nor the biaxial stressed condition. In addition, it does not include 
eccentric loading conditions nor pertain to low ductility steels where special 
provisions need to be considered. 

5.2.2 The Actual Uniaxial Condition 

The actual uniaxial condition is a httle more conplicated than the 
condition modeled by AISI. Firstly, when considering the actual initial 
support condition, another variable is introduced to the standard equation. 
Figure 5-3 shows the revised derivation from a free body diagram of an actual 
system resisting pullover. The equation is very similar to equation 5. 1 ; 
however, the angle of deflection, 6, is introduced to the equation: 

P„^^2t,d^F^,sm(0) (5.2) 

And is directly affected by the in-plane strain of the panel, e. 



Equation 5.2 does predict the uniaxial, concentric pullover strength of high 
ductility steels quite accurately; however, when used for high strength, low 
ductility steels (for example grade E steels) it fails to provide accurate results. 



102 

The reason is quite simple. Consider one steel plate with moderate 
strength and high ductihty and another steel plate with high strength and low 
ductility. Each plate contains one hole with a smaller diameter dowel placed 
within each hole. Consider the dowel material a superior material with 
respect to the steel plates (Figure 5-4). While restraining each plate in one 
direction, each dowel is restrained in the other such that a projected area of 
bearing exists between dowel and plate. Intuitively, the plate with less 
ductility provides a smaller projected area of bearing than the plate with 
higher ductility because the brittle steel plate fails to conform to the dowel 
bearing on it. 

The same condition can be applied to the actual system in question where 
two panels, each with one hole containing one stud of superior strength, are 
stressed in tension (Figure 5-5). The ductile panel deforms around the stud 
such that the projected tensile area is approximately equal to the panel 
thickness times the screw head diameter, tjdy,. Note that this is the projected 
area presently used in the standard pullover equation. The brittle panel 
provides a smaller area of projection that is equal to the panel thickness times 
the difference between the screw head diameter and the hole diameter, ti(dy,r 
d^. This particular provision does not exist in section E4.4.2. 



103 

Given the unique behavior of grade E steel, the screw head diameter 
variable d^ should be replaced with the projected distance variable di thus, 
changing equation 5.2 to: 

P^^2t,d,F^,sm(0) (5.4) 

Where: 



d, = d^ for ^ > 1.08 
Fy 

d,={d^-d,)for^<\m 
Fy 



(5.5) 



Equations 5.3 through 5.5 represent the pullover strength of a panel, 
concentrically loaded, for all steels subjected to uniaxial stress. 

Eccentrically loaded panels are more complicated to model and require a 
different approach. Figure 5-6 illustrates an eccentrically loaded screw/? that 
stresses a panel with spans a and b. The figure also shows an elevated view 
of a typical hole and screw head perimeter. Three fundamental modes of 
failure exist around the hole and they are labeled crj, cr2, and crj 
respectively. Given the screw dimensions (i.e. head diameter and the stud 
diameter), the span ratio b/a can be predicted by summing the moments at 
each cracked section. This b/a ratio states which projected distance, dj will 



' \. f 



104 



apply to the eccentrically loaded system. Projected distances for an 
eccentrically loaded system are as follows: 

d.=d. (5.6) 



a 



^d^^d,^ 



.d^-dj 

di = yjdj - d, 



d.+dA^b . 1 ,2 .2 (5.7) 

\d^-dj a 

Please note that equations 5.6 and 5.7 do not apply to grade E steels 
because, grade E steels are brittle and fail to deform around the stud of the 
screw. Since: 

(d.-d,)<^dj-d,', d,={d^-d,)forall- (5.8) 

a 

Eccentrically load systems will produce two independent angles of ' 

deflection. If each span has the same stiflftiess, intuitively the shortest span, a 

will initially experience ultimate strain and produce the greatest angle of 

deflection, 6a. The greater span, b will produce a smaller angle of deflection, 

Ob and thus, an in-plane strain of lesser magnitude. Therefore, due to the laws 

of equilibrium, only the smaller span will experience ultimate stress, Fui while 

the larger span will experience less stress, Fe. This behavior will modify the 

pullover condition (Figure 5-7): 

Pna.- = iAiK^ sin(^J + F, sin(^,)) (5.9) 

where Oi, can by determined from this geometrical relationship: 



105 



a b 



and where: 

'cos(^j' 



F. = Fu^ 



(5.11) 



.cos(^j; 

By combining equations 5.3 through 5. 1 1, the uniaxial stressed condition for 
pullover can now be defined for all steels as: 



Concentric Condition 
1.) Calculate sin(<9) 



sin(6') - '-^ ' 



(. + 1) 
2.) Determine dj : 



Fu 
Fy 



Fy 



nov 



3.) Solve for P„ 



Eccentric Condition 



1.) Calculate ^^and Ob 



sin(^J 



a 



h 



tan(^J tan(^J 



2.) Calculate Ff 



106 



F. = F. 



Uos(6'J>' 



3.) Determined; 



//^>1.08 



l<-< 
a 









d,=d 



<-<cc^d,^^dJ-d,' 



//^<i.08 
Fy 

dr={d.-d,) 



4.) Solve for P„ 



P_ = f ,</, (F„, sin(^, ) + F, sin(^, )) 



107 
5.3 Biaxial Tension 
Pullover, due to biaxial tension, is the most common failure condition 
found in through-fastened metal roof and wall systems (Figure 5-1). 
Ironically, no design criteria exists for biaxial pullover. This partially 
explains why the AISI specification is unconservative and fails to provide an 
accurate means of predicting pullover strength. The objective was to provide 
the design criteria for biaxial pullover in an actual system. 

5.3.1 Biaxial Stresses 

In order to predict the biaxial pullover strength, it is first necessary to 
determine the biaxial stresses that develop within the panel. Stress is defined 
as follows: 

f = Ee (5.12) 

Where E, is the modulus of elasticity, and ^ is the strain. 

Consider a typical metal panel with a longitudinal stiffness, £"«, and a 
transverse stiffness, Ep (Figure 5-8). The longitudinal in-plane stresses that 
develop in the panel are defined by equation 5. 12 and can be determined if a 
stress-strain diagram of the panel material is provided (see Chapter 2 for 
tensile test data). The transverse in-plane stresses are affected by the 



• 108 

geometric configurations of the panel (i.e. the web stiffeners and the valleys). 
Transverse stresses can be determined from the cross-section of the panel by 
means of the standard tensile test or several structural analysis methods. 
Exan^les include the direct stifihess method or finite element analysis of a 2 
dimensional frame (Figure 5-9). Transverse in-plane stifftess, Ep , will 
typically be less than longitudinal in-plane stiffiiess, Ea. 

In-plane strains are affected by the span lengths of the panel. Figure 5-10 
illustrates an eccentrically loaded system with four independent span lengths 
lamax, Icamn, Ifimax, Ifimin respectively. Each Span length will produce a unique 
angle of deflection and in-plane strain. Recall Eccentrically Loaded Systems 
in Section 5.2.2 where two independent angles of deflections exist. 
Intuitively, the shortest span a produces the ultimate angle of deflection and 
the ultimate in-plane strain. Conversely, the longest span b produces the 
smallest angle of deflection and the smallest in-plane strain. However, this is 
only true for the uniaxial case where both spans have the same in-plane 
stiffness. In a biaxial case, where Ep may not equal £«, identifying the span 
that initially fails in the system is a little more complicated. In a system 
where Eamax = Eamin and Epmax = Epmin, oc,riax or Pmax coutrols, choosing the 
ri^t span is critical (Figure 5-20). Given the ultimate strains for each span 



109 

^amaxu and Sfimwcu, the ultimate angles of deflection a„uixu and ^^axu can be 
determined using equation 5.3. Both spans should produce the same 
deflection A and thus: 

4n„x tan(a „„ J = /^„„ tan(/?„„, ) (5. 13) 

If this is true, both spans will fail simultaneously. However, this is usually 
not the case. By defining Aamaxu and Apmaxu as: 



the span that initially fails is identified as follows: 

f /?m« = Sfin^.. far A^ > A^ 

£am^ = ^a^^u far A^ < A^ 

hi a system where Eamax ^Eamin ^Efl„^^ ^Epmln- 

A„„„„ ^ A„^„ and A^„„„ < A^^„: 
F "=■ p fof A <c A 

amix amixu -» or mix u — /?m«.\u 

A„™^«<A„^„ and A^^„>A^^,: 
£ = £ for A < Afl 

a nux aauxu J a max u ^^pmmw 



^max ^nux« y^ a min u — ^mixu 

f — f /(yr A < A 

amm aminu J a min u ~ Bmtxu 



(5.14) 



(5.15) 



^fimm - ^fiminu f^^ ^a mini, - ^^minu i^^^) 



110 

l^arn^u > Km^u and A^^„>A^ 

^/?miii - ^>9miii« y^r ^amnu-^p 

Section 5.2.2 explained the relationship between in-plane strain and the 
angle of deflection. Expanding this principle further, the biaxial case 

produces a„uzx. CCmin. Pmax. Pmin and €amax> ^cmiw Spmax, ^fimin whcrei 



/ 



*• a mix » ^ a min ' ^^mix ' ^^ n 



-1 (5.17) 



Given both the stiffiiess and strains of the system, the stresses can now be 
determined at each span. The following equations define longitudinal stresses 
for an eccentrically loaded system based on an approximate, bilinear stress- 
strain distribution of the panel material (see Chapter 2 for the biaxial stress- 
strain distribution of each panel material tested): 

F ^F +E (e -£ ^ ^^-^^^ 

a mix. a mm amix>',amin>' /?amix,pamin V^ amix. amin amixv.ammv/ 

foK £ > £ 

J ^amix,amiii " a mix v,a min v 

Transverse stresses are more difficult to define. The transverse stiffness, 
Ej3 may be determined from a tensile test or a theoretical model. Figure 5-9 
illustrates the cross-section of a typical panel used for simulated pullover 
testing. A stress/strain curve generated from a tensile test is included. Note 



Ill 

the non-linear relationship of £> The transverse stifihess approaches the 
longitudinal stiffness as the load progresses to the ultimate capacity. Like the 
longitudinal stiffness, transverse stiffness has a linear-elastic range which 
exists from to 0.56 ksi for this particular material specimen. Figure 5-1 1 
shows the derivation of transverse stress based on a bilinear stress/strain 
distribution which is defined as follows: 



^finux,fimm Pma.y.fiimay ' ^ pPma^pPnauK'' Pma^Pnan Pnux.y,pnmyJ 

JOr £pBax,Pmm '' ^/Jnuxv.^minv 



(5.19) 



5.3.2 Concentric Loading 

Figure 5-12 illustrates a concentrically loaded system. Two failure modes 
often associated with this system are included. The failure modes are 
affected by the tensile stresses which develop around the fastener. The 
failure modes are defined by angle ^ as: 



^ = atan 



fF ^ 



(5.20) 



When the longitudinal stress is much greater or less than the transverse 
stress, (f> equals 90° or 0° respectively. This generates the first failure mode 
which is most common in through-fastened metal roof and wall systems. The 



112 
reason is quite clear. Most panels will have far less transverse stiffness than 
longitudinal stiffness. In some cases the stiffness ratio, Eo/E p, may be 100 or 
more. Since the screw spacing is typically 5 fl. longitudinal by 1 ft. 
transverse, the span ratio, IJlp , is typically around 5. This means that the 
span ratio, in general, does not overcompensate the stiffness ratio and thus, 
the stress ratio, Fa/Fp, is often quite high. As a result. Equation 5.20 will 
produce a high stress ratio generating the first failure mode where ^ equals 
0*'or90''. 

In the event that the stress ratio is approximately equal to 1, ^ will equal 
45°. This failure mode has been observed during several tests. However, its 
cause was not affected by screw placement nor panel type. It was caused by 
the buckling failure of the web stiffeners which may occur long before 
pullover (Figure 5-21). If the web stiffeners buckle before pullover, the 
transverse stifl&iess becomes equal to the longitudinal stiffness. Given the 
right conditions, this would allow the stress ratio to approach unity and thus 
generate the 45° failure mode. Therefore, if the compressive stresses that 
develop within the web stiffeners resisting pullover exceed the critical 
buckling stresses, if> will equal 45° and Fc/F^ will equal 1 . If the con^ressive 
stresses that develop within the web stiffeners resisting pullover do not > 



, ,/113 

exceed the critical buckling stresses, the stress ratio Fa/Fp may or may not 
equal 1. This would then depend on the screw placement and the panel 
geometry. The relationship between panel buckling strength and panel 
pullover strength is beyond the scope of this research. Further testing is 
necessary before incorporating panel buckling into the present design criteria. 

Due to the fundamental laws of equih*brium, the concentrically loaded, 
biaxial stressed system provides the pullover strength equation: 

P„^ = 1{F,A^ sin(a) + F^A^ im{P )) (5.21) 

Where Aa and Ap are the projected areas and both are ftinctions of (f) . They 
are defined in Figure 5-13 as: 

A^ = t,d„ 

^P = t^dp (5^23) 

where da and dp are: 



(5.22) 



d^ = d^ cos((f) ) & dp=d^ sm{<l> ) for-;:r> 108 



Fy 



d^={d^-d,)cos{(f>) & dp={d^-d,)M<l>) for—<\m ^^''^^^ 

Fy 

The pullover equation can now be defined as: 

P^ = 2(Fj,d, sin(a) + F^t^d^ sin(;9 )) (5.26) 



114 



5.3.3 Eccentric Loading 

Figure 5-12 illustrated a concentrically loaded, biaxial stressed system 
with two failure modes associated with the system The failure modes are 
affected by the tensile stresses which develop around the screw and are 
defined by angle ^ . This principle is also true for the eccentric condition; 
however, each projected distance da and dp , may be off-centered depending 
on the longitudinal span ratio, lamin /lamax, and the transverse span ratio, 
Ipnunllpmax, rcspcctively. See Figure 5-14 for possible failure modes 
associated with the eccentrically loaded, biaxial stressed system. 

Expanding equations 5.6 and 5.7 for the biaxial condition: 



1< 



< 



1< 



/ 



/*« 



/. 



< 



d.-d 



^d^-d, 
fd+dA I 



d^ = d^ cos((/5 ) 
dfi = d^ sin(^ ) 



<-^<oo -> d^ = yfdj^ cos(<f> ) 



d.-d 



<^<^^d,^^dj^sm{<f>) 



h^ V 



(5.27) 



(5.28) 



As noted in equation 5.8, grade E steels do not apply to the above conditions, 
histead: 



115 



d^=(d^-d,)cosi<f>)forall^ 



^f^ (5.29) 

d, = id^-d,)sm{</>)forallf^ 

Due to the fundamental laws of equilibrium, the eccentrically loaded, 
biaxial stressed system provides the pullover strength equation: 
Pna. = Kn^A sina^ + F^^A^ sinor^ t ^/»m«^/j sm/3^ + Fp^Ap siny9„„ (5.30) 
Substituting equations 5.22 and 5.23 into equation 5.30, the pullover equation 
can now be defined for an eccentrically loaded, biaxial stressed system as: 

Pna. = F,^t,d^ sin(a^) + F^^t.d^ sin(a^) 

+ Fp^t,dpsm(fi^) + Fp^t,dpsmij3^) ' ' ^ 

The biaxial stressed condition for pullover may be defined for all steels as: 

Concentric Condition: 

1.) Find the span that fails first: 



iSa.^ 






iSpu 






A^ =/„tan(aJ 



Sp = ^Pu for A^ > A^ 
^a = ^» for A^ < A^ 

2.) find sin(« ) and sm{fi): 



116 





k(^a+2) 




H-.+ir 


tan(/?) 


^A^p^A 


tan(a) 



3) Find £„ and sp : 



£„ - 



'(l-sin'(a)) 



((l-sinV)). 



-1 



4.) Find Fa and F/? : 

F„ = ^,„f „ /or £„ < f „ 

F„=F„.+£^„(f„-f^) 
^/j = E,p£p for Bp < e^ 



^p - Ppt,'^ ^ppK^p ^fy) 

for Sp > e^ 



5.) Find^ 



117 



^ = atan 



'^1 
.FJ 



6.) Find da and d^ : 



d^=d^cos(^) & d^=d^sm((f>) /or -^> 1.08 



d,=id^-d,)cos{(f>) & ^^=(c/,-(/Jsin(<;J) /or -^ < 1.08 



7.) Calculate P;,ov : 



Pna. = 2iFj,d, sin(a) + F^t.d^ sm(y9 )) 



118 



Eccentric Condition: 

1 .) Find the span that fails first: 



„;_/«, \ I a mix K V a mix « / 



sm(/?„„„ ) =J— — ^ ^ 



^amin« =4mi«tan(a^J 

^fima-^fima.^ faf ^a mix 1, - ^^ mix « 

omix ~ ^amau J"^ ^anaxu — ^/Smixu 

'^amix ~ ^amixu J^^ ^anaxu — ^fiamu 



119 



amin ammu J^ amjau — y?maxu 

amin aminu J^ ^aouau ~ Pmmu 

Z..) rinu Umax J Uffiin ? Prnax ■> Pmin • 



Is (s + 2) 
(^.«,« + 1) 



sm(/?^) =J— r^ -r^ 

If (e +2) 

\ mm / ,1 / \2 

(^amin + O 



I /)miii ^^^min + 2 j 

tan(a_) tan(a^) tan(>9^) tan(yff„J 



amin ^max ^min amax ^max ^tnin ^ min a max a min ^ max a max a min 



J.) rUlQ Samax t ^amim ^fimax^ ^fimin 



120 



Vnim 



'^imx 



'(l-sm^(«„j). 



'(l-sm^(a_)) 



'(l-sin^O^^)). 



((l-sin^ (/?_)) 



-1 



-1 



'f.) rinu r amax •> ^ amin i ^fimax ? ^firmn '• 

crnMX '-'^ff mix "a mix 7"' ''amix — *'amix,v 

'^amix ~ *^eomm^amix "*" ^pamix V^crmix ~ ^ am»x.y) J^^ ^ ama. ^ ^ 



mix amixy 



F" ^ F P fny F <i P 

amin eamin amin y^' amin — ^ aamy 



^^mix '^tPmtx.^fima f^f ^^n.„ ^ ^ PmMx.y 
'finux ~ ^efimtx^fimtx "*" ^p/?m«x V^^mix ~ ^ flouxy 



) /O^ ^/Jm«. > £fi„^y 

^finun ~ ^e^min^^mm /'-'^ ^/?mm — ^^mio.v 



5.) Find ^ 



F =F +F 

a ■* a mix ■■ amm 



^ = ataii 






6.) Find da and dp : 



121 



F^ 



1< 



>1.08 



< 






' d.+d, ^ 
\d^-dj 

\d„-dj 



d^ = d^ cos(<;> ) 
dfi = d^ sin(^ ) 



< J^EL < 00 ^ ^^ = .JdJ^dJ sm(^ ) 



^^.+^.^ / 



^d^-dj 



fivaax 



<1.08 



<^„ ={d^-d^)co^<f>) for all 



dp = (d^-d,)sm{^ ) /or a// 



amin 


'a mix 


'^min 



fimax. 



7.) Calculate P„ov • 



Pno. = ^.„„^<^a sm(a„«) + F„^?,</„ sin(a^) 



122 
5.4 Pullover Strength And Steel Strength 
The relationship between pullover strength and steel strength is unique and 
warrants cautious consideration when designing against pullover. High 
strength steels will not always provide a higher resistance to pullover than 
low strength steels. Surprisingly, in some cases, high strength steels can be 
detrimental to a through-fastened metal roof or wall system. The reason may 
not always appear obvious but it is due to the brittle nature of high strength 
steel alloys. In general, high strength steels are less ductile than low strength 
steels. They have limited deformations and ultimate straining capacities. The 
relationship between ultimate strain and yield strength varies and it depends 
on the selected alloy. Figure 5-18 illustrates one relationship for ASTM 607- 
85. 

The simplest representation of pullover strength, as a function of steel 
strain, is obtained by substituting equation 5.3 into 5.2. Hence: 



P.^. = 2t,d..F.. 



\e{s + 2) 



1"h-«u|, .2 (5.32) 

(f + 1) 

Pullover strength is a function of both ultimate strength and ultimate strain. It 
is further understood that ultimate strength, F„/, is directly proportional to 
yield strength, Fv, such that: 



123 
Fu^^CF^ (5.33) 

where C can range from 1 .05, for low ductility steels, to 1 .2, for high ductility 
steels. Considering this relationship and substituting the values from Figure 
5-1 8 into equation 5.32 (i.e. the ultimate strain and yield strength values), the 
following relationships can be identified in Figure 5-19. 

As noted earlier in Figure 5-18, ultimate strain decreases as material 
strength increases. However, material strength contributes to pullover strength 
at a rate ranging from: 

1.05F, to \2F^ (5.34) 

and ultimate strain reduces pullover strength at a rate: 



ie + l) 

^ ' (5.35) 



Since both factors effect pullover strength at different rates, the 
contribution from material strength will eventually equal the reduction from 
material strain. This state is called "Pullover Balance" and it represents the 
optimal material for resisting pullover. Figure 5-19 shows that ASTM 605-85 
grade 70 steel has the greatest pullover strength in the series. If a higher 
grade material from the same alloy is selected, the reduced ultimate strain 
factor will eventually overcompensate the increased ultimate strength factor. 



124 
thus reducing the pullover strength. This decline in pullover strength is 
illustrated in Figure 5-19 for ASTM 605-89 steels, grade 70 through 80. 



125 



Fixed 







Fixed 



O 



o 



Fixed 







O 



r 

■0 

i 



o 



o 







Fixed 



O 

t 






— Fixed 



Fixed 



Screw Subjected To Biaxial 
Tension In Panel 



Screw Subjected To 
Uniaxial Tension In Tile 



Figure 5-1 - Uniaxial Stress And Biaxial Stress 



FujA 




Stud,(j)= di 




Free Body of Standard 
Pullover Test. 



Head, ^ = d* 



Hole, (t> = dh 



T IK - 0: P„„. = 2F,,A where A = t,d^ 
Applying A R.F = 0.75 



P„„, = 1.5/,c/,F„, 



Figure 5-2 - Derivation Of Equation E4.4.2.1 



126 



Fu,A 






FuiA 





lf=el„+l^ & l/sm\e) = il/-0 



sm\0) = 



_H+lo) -Iq e'lo'+elo' 



2 . ; 2 



(eL+Lr eX+2eC+l^ 



sm\0) 



s'^+le e(e + 2) 



s'+2e + \ (el^+IJ 



-> 




^ ^^- = 0: Pno.. = 2F^,A siii(^) where A = Ld, 



l"w 



^„<n. = 2/,^./;, sin(^) 



Figure 5-3 - Derivation Of The Actual Pullover Equation For Uniaxial Stress 



127 



Dowel 



Projected Distance, d| 




Dowel 



^<_1.08 
Fy 



Projected Distance, d 



Hole, dh 



Fu 

-^ > 108 

Fy 



Hole, dh 




Figure 5-4 - Difference Between Brittle Steel Behavior And Ductile Steel Behavior 
(Dowel In a Steel Plate - Tensile Interaction) 





di=d^- d, 

^.1.08 
Fy 



d,=d 



Fu 
Fy 



>1.08 



Figure 5-5 - Difference Between Brittle Steel Behavior And Ductile Steel Behavior 
(Actual System Resisting Pullover) 



128 




a + b 
t 



T 
p 



a 



\a + b 






-^: 



a + b 



a 



a + b 




IM,,, =0: 



a + b 



a 



\a + b 



P(fJ= — T /'(''h)^- = 1 



a 




^Mcr2 = 0: 



\a + b 



P^r^-r,) 



f_a_\ 
\a + h) 



P{r^+h)-^- 




IA/^3 = 0: 



* V(0) = (-^b(^) 



a+b 



a+b 




Figure 5-6 - Eccentrically Loaded System Resisting Pullover Which May Cause 
One Of Three Fundamental Modes Of Failure 



. 4 



129 



i 



2 2 







a 



d. +d, 
\d^.-d,j 



d.^d. 



\d^-dj a 



d,=d 



< - < 00 -^ c/, = yidj-d, 



Figure 6 ~ Continued 



Fu,A 



\i " I 




Fyl 



A = atan(^J = 6tan(6>J 



a 



tan(^,) tan(^J 



Fx,=F^,Acos{0J 
Fx,=F^AcosiO,) 



K = K, 



{cos{0^)J 



t IFv - 0: /? = f;, A sin(^, ) + F,>t sin(^, ) 



where: A = t^d, :. 



/7 = r,t/,(F„,sin(^J + F,sin(^J) 



Figure 5-7 - Eccentrically Loaded System Which Generates Two hidependent 
Angles Of Deflection And Two Independent hi-Plane Stresses 



■''J 



130 




Figure 5-8 - Simplified Model Of Metal Panel 




r^nOooe 




I. 




Fa . 

(ksi) 


i 




p 




66. 














^^'''^''^^^ 






55 


/ 




' 


/ 






V 



0.0833 0.167 


0.24 Ep 


0.0019 0.24 


Ea 




(in/in) 




(in/in) 


Transverse Stiflfeess 




Longitudinal Stifftiess 





Figure 5-9 - Simplified Model Of Panel Cross-Section 



131 




Given Equation 5.3 - Strain Can Be Derived As 
A Function Of The Deflection Angle: 



Sin(^) = 



_ / g(£ + 2) . s(s + 2) 



{e + \r 



. sm\0) = 



{e + lf 



For The EccentricaJly Loaded, Biaxial System: 

~ min ' '*ni»x ' "min ' A-'i 



nun ' " max " ' 



gftitn 
fitnih ^ 




-1 

-1 

-1 

-1 


/ 1 


\fl-sin^(«.J 


/ 1 


Vl-sin^(«m.x) 


1 


/ 1 


i|j-sin^(;^..J 






1 



l-sin'(^) 



l-sin(6') 



£ - 



l-sin'ie) 



Figure 5-10 - Eccentrically Loaded System With Four Independent Span Lengths 



132 



Longitudinal Stress : 



F = E F 

amax^amm Qfmax,aimn amix.a:min 



E = E 

iznux,ainiii eamvLeamm 



i, forO< E„ 



■ < £ 
max^anun — amaxy.armiDV 



anMX,aniiii pamxi^pajaia /'-''" ^a 



> E 

max.aiii]n amax.v,amiii>' 



From Figure 9 



anux.amni ?ffm«x,eamin^aiiiix.amiii J^^ ^ 



<e 

amix,ainm amix v.crmini' 



aniix,(2miii anux.v.amin.v "'' ^;)aiiMX,pamiii V^amix,aiiiiii ^ amt\y.amxDy) J^^ ^a 



> £ 

iiux,aiiun a max 1-. a mini- 



Transverse Stress : 



F - F p 



pisax.,Pmm '^ ePmt^ePnua jOf U < £'/jni»x,^mm - ^^max>',^min.v 

^ F 

Ptnax,atnm Pnaxy^Ptamv 



Pnux,Piim ^ pPaux^pPmn J^^ ^/?m.»/.mm ^£ 



From Figure 9 



Pmvi,pmn ~ ^e^max,«^miii^^max,^min J^^ ^ Pnux,Pmia — ^ Pnuxy,PmiBv 

Pm^PmiD - Pmn.y,PBuny '^ ^ pPnax.pP mm i^ PmMX.P am ~ ^ Pmtxy.pmmy) fa^ ^^raax,^miii > ^ pnaxy.Pnany 



Figure 5-1 1 - Transverse and Longitudinal Stress Derivation 
(Bilinear F/e Distribution) 



133 



tlK =0: 

P„^. = 1{P, s\na + Pp siny9) where: 



Pnc- = 2(F„ A^ sin a + FpApS\nP) 



A-/„tan(a) = /„tan09).-. 



tan(a) _ tan(y9) 



/« 



/ 




\ 


> 


. 


Fa 


■ 


• 


A\ 




}■< 


b^ "^ 


v' 






/ 


^;r~X 


\ 












V 




/ 






.X 
< 










' 


" 


" 


1 










Figure 5-12 - Concentrically Loaded System 



Fa » Fp or F„ « Fp 
(f> =Q° or (l> =90° 



134 



A„ = td„ & A„= t,d. 



dfi = [2(r, - rj sin ^] + [d, sin ^] = d,. sin (/> 



Ffi 




(r^- r^sinip 



di^^ 



(r^- rh)sm^ 



t 1 T T 1 t t T 



'■»-''* 





-H^ 



-+^ 



(r,.- rh)cos^ 4cos^ ^r„,- /-a^cos^* 



TtTTttTTt 




Conservative Approximation 



Figure 5-13 - Projected Areas And Distances 



135 




<^ = 45" 



< 



d^+d. 



d-d, 



J 



d.+d, 

^d^-dj 



-omin 
< < 00 



finax 




a 







^-45" 



d^ + d. 



yd^-dj 



< 



< ac 



<+d, 
Vd^.-dJ 



< < 00 



/ 



Pmtn 



There are variations of "peeling" which 
occurs after crack propagation. The given 
patterns were obser\ed during testing. 
(See Figures 15 through 17 for photos). 



<l> = 0° 




(/> = 0° 



d-d. 



< < 00 






d.+d, 
.d-d. 



<d^.-dj 



<_£i5SL<Qo 



. Bmm 
< < 00 



^mix 



Figure 5-14 - Filure Modes For The Eccentrically Loaded Syst 



em 



136 




Figure 5-15 - Combined Concentric And Eccentric Failure Modes 



137 




Figure 5-16 - Concentric Failure Modes 



M 



138 




Figure 5-17 - Eccentric Failure Modes 



139 



Yield Strength Verses Ultimate Strain For ASTM 
607-«5 Steel, Grades 45 - 80 ksi 



0.25 



c- 0.2 



T 



£ 0.15 



CO 

a 
E 



0.1 



0.05 



40 




Yield Strength (ksl) 



Figure 5-18 - Yield Strength Verses Ultimate Strain For ASTM 607-85, 
Grades 45-80 



Yi 

1.4 - 

- 1.2- 

a. 

E 1 

w 0.8 

S! 

5 0.6 

(0 

§ 4 
o 

3 0.2 


4C 


eld Strength Verses Pullover Strength For ASTM 
607-85 Steel, Grades 45 - 80 ksi 


"Pullover Balance" -V \ 


1 H . _ 1 

5 50 60 70 80 . 
Yield Strength (ksi) 



vf 



Figure 5-19- Yield Strength Verses Pullover Strength For ASTM 607-85 
Grades 45-80 




«m«« =asin 



a max u V tr ma-x u / 






tan(a„„) = 



tan(>9_) = 



a max 

A 



fimax 



for a^^= a^^^ & y9„„ = y5^^„ ^ 



^am« tan(a„„„) = /^^^^ tan(y?„^^ J 



Not Always The Case 



140 



* * 




O^inaxu 



pmax 



^Bmaxu 



6prr 



^amaxu " 4max tan(Gr^^y) ^/?maxu " '^max ^^(P m»xu) 



^^max ^^maxii /^^ ^amaxi/ - ^fitoMx^u - BccaUSC Abi^^ OcCUTS FifSt 



ormax ^amaxH J^^ ^amaxu - ^>?max« - BccaUSC Aanaxu OcCUTS FirSt 



Figure 5-20 - Finding The Span That Fails First If Ea„,ax = E^^ And Ep„^ = E 



pmin 



141 




Figure 5-21 - Web Stiffener Buckled Before Pullover 



CHAPTER 6 
FIELD INSPECTIONS 

6.1 Existing Systems 
Through-fastened metal roof and wall systems are very economical and 
easy to install. There are numerous catalogs that provide systems with a 
variety of shapes and colors. To maintain the aesthetics and continuity of 
buildings, many prefabricated systems include matching coping, flashing, 
gutters, and other additional cladding. A variety of systems are shown on 
Figures 6-1 througji 6-4. Many are used for commercial buildings, hangars, 
and store fronts. 

For the reasons described above, throu^-fastened metal roof and wall 
systems are growing in popularity. Today, they are some of the most common 
systems used for structural framing and cladding. 



6.2 Catastrophic Failure 
It is obvious, after analyzing the data given in Chapters 3 and 4, that 
engineers have failed to predict pullover in through-fastened metal systems. 



142 



143 
This is a severe problem because, pullover, in most cases, is the governing 
failure condition. In some cases, present systems are structurally unreliable. 
Correcting this problem is vital to the future of this unique construction 
method. 

Chapter 5 provides a design criteria for pullover that works effectively and 
it is highly suggested that it be adopted into the current AISI specification. 
This new criteria would replace the existing criteria in section E4.4.2. A 
statistical comparison of the new design criteria and the existing test data will 
be discussed in Chapter 7. 

Aside from the existing test data, a field inspection of a typical through- 
fastened metal system was performed after a severe windstorm. The metal 
building was a supermarket located in the Virgin Islands, specifically, on the 
island of St. Thomas (Figures 6-5 and 6-6). 

On September 15, 1995, Hurricane Marilyn swept across the island. 
Winds were gusting up to 135 mph and the storm lasted approximately 12 
hours. The damage of the building was extensive. Initially, all of the glass 
windows and doors in the front of the building were blown out. This created 
a large pocket in the building that trapped the incoming wind. There was no 
exhaust or vent in the structure that could relieve the building's internal 



144 
pressures. Most of the damage was created from the following gusts that 
lifted the entire structure from the foundation. The amount of uplift is 
uncertain; however, when the structure returned to the ground it collapsed on 
itself. There were many explanations for this dramatic and catastrophic 
failure; however, the investigation focused primarily on pullover which played 
a unique role. 

As intemal pressure grew inside the building, many extemal panels blew 
off the roof and walls (Figures 6-7 and 6-8). This was devastating to the 
structure because the diaphragm was lost and the exposed mainframes were 
left to resist the applied loads. Although the mainframes are typically 
designed to resist some of the loads, without the extemal wall panels and the 
roof diaphragm they cannot resist all of the loads. The metal panels typically 
provide most of the building's shear resistance to lateral wind loads. 
Mainframes typically resist only a fraction of the shear stresses (normal to the 
mainframes) that develop in a laterally loaded structure. As a result, the 
mainframes failed catastrophically (Figures 6-9, 6-10, and 6-11). 

As expected, pullover was the primary failure mechanism associated with 
the loss of the roof diaphragm and the extemal walls. Figure 6-12 shows the 
exposed girts and purlins with remaining fasteners that once anchored the 



145 

exterior panels to the framework. Figures 6-13 through 6-18 show evidence 
of pullover in metal panels that remained near and around the structure. 
Some cracking patterns show evidence of concentric failure which initially 
occurred, while others show eccentric failure which typically occurred later 
and with less resistance. 

The photographic evidence supports the pullover problem in the field but it 
does not suggest that the system is inferior. The through-fastened metal 
system can be very effective in heavy wind if the correct number of fasteners 
are placed in the appropriate areas. The evidence also suggests that a better 
understanding of the system is necessary. Designers must be able to calculate 
and predict the allowable pullover strengths of metal panels prior to 
construction. This would be possible if AISI adopts the design criteria 
provided in Chapter 5. 



146 




Figure 6-1 - Store Fronts And Canopies 



147 





Figure 6-2 - Hangars 



148 




Figure 6-3 - Storage Facilities And Warehouses 



' V 



149 



.'»' 




Figure 6-4 - Commercial Buildings 



150 





Figure 6-5 - Grand Union Supermarket, St. Thomas, U.S. Virgin Islands 
(Front View) 



151 




Figure 6-6 - Grand Union Supermarket, St. Thomas, U.S. Virgin Islands 
(Side View) 



152 




Figure 6-7 - Metal Panels Removed From Exterior Walls 



' 5 < i. 



153 




Figure 6-8 - Metal Panels Removed From Roof 



I t 



'AUt 



154 




Figure 6-9 - Catastrophic Mainframe Failure 



155 




Figure 6-10 - Catastrophic Mainframe Failure 



156 




Figure 6-1 1 - Catastrophic Mainframe Failure 



157 




Figure 6-12 - Exposed Girts And Purlins 



,.."•■ *.f'\- 



158 




Figure 6-13 - Pullover Observed In Metal Panels 



159 




Figure 6-14 - Pullover Observed In Metal Panels 



160 




Figure 6-15 - Pullover Observed In Metal Panels 



161 




Figure 6-16 - Pullover Observed In Metal Panels 



162 




Figure 6-17 - Pullover Observed In Metal Panels 



163 




Figure 6-1 8 - Pullover Observed In Metal Panels 



V i^f't*^'*' 



164 




Figure 6-19 - The Palm Tree Stands Alone 



CHAPTER 7 
CONCLUSIONS AND RECOMMENDATIONS 



71 Reduction Factors For The Standard Test And Equation E4.4.2.1 
The Standard Test and Equation E4.4.2. 1 are presently two methods that 
predict virtually the same nominal pullover strength. This is due to the 
equation's origin, which can be derived from a free body diagram of the 
Standard Test apparatus. Both methods are unconservative. Initially, the 
intent of the research was to provide reduction factors for both methods. 

The average load capacities of self-drilling screws were calculated for 
each specified condition as seen on Table 7-1 for Component Tests, and 
Table 7-2 for System Tests. 

Table 7-1 shows average load capacities for four independent conditions. 
Fixed End Concentric Loads and Eccentric Loads, Condition 1 , cannot be 
used to determine the reduction factor. The Fixed End Concentric Load data 
cannot be validated because only one data point was recorded for each panel 
type. In addition, an actual system contains a fixed boundary for each side of 
a metal panel. The Fixed End Concentric Tests provided only two fixed 

165 



166 
boundaries. The other two boundaries permitted lateral, in-plane 
displacements. The Eccentrically Loaded Component Tests, Condition 1, 
modeled systems in an unrealistic manner. The applied eccentricities were far 
greater than those ever observed in an actual installation. The remaining two 
conditions were acceptable for determining a reduction factor. Table 7-3 
shows the calculated reduction factor for each panel tested. 

Table 7-2 shows average load capacities for both concentric loads and 
eccentric loads. Due to system test observations, where initial failures were 
randomly eccentric or concentric, it was decided to average both conditions 
together. In some cases both conditions occurred simultaneously; therefore, it 
was unnecessary to calculate the mean load capacities for each condition. 
Typically, initial system failures generated maximum load capacities and thus, 
the average maximum load capacities were calculated. However, it would be 
unconsevative to calculate reduction factors from these quantities because 
they would not account for the subsequent failures, which occur at lower 
loads. Therefore, the decision was made to calculate the minimum load 
capacities which were later used to calculate the reduction factors (Table 7- 
3). 



167 

The System Tests provided lower load capacities than the Component 
Tests. This was primarily due to a change in boundary conditions. The 
System Tests used a fixed boundary condition at each side of the metal panel 
with the exception of the edge screws where only one free boundary existed 
for each edge screw. The Component Tests used two fixed boundaries and 
two boundaries that restrained only vertical displacement. Lateral in-plane 
displacement allowed additional deflection to occur during the load cycle, 
which increased the load capacity of each fastener. 

The dissimilarities were also associated with the applied loading 
conditions. The System Tests provided a uniformly distributed load that was 
applied directly to the metal panels. This load application is consistent with 
that observed in an actual installation. The Component Tests used a 
concentrated load that was directly applied to the fastener. Component Tests 
were only simplified models; therefore, the data accumulated from these tests 
do not represent the load capacities identified in actual installations. 

The reduction factors determined from the Component Tests are not 
recommended for the Standard Test nor Equation E4.4.2. 1 . The test 
procedure does not accurately model a typical installation. 



168 
The System Tests provided the most ideal reduction factors and they are 
most conservative. The System Tests provided reduction factors ranging 
from 0.235 to 0.321. The testing data suggests that the Standard Test and 
Equation E4.4.2.1 predict load capacities for a single fastener, in a through- 
fastened system, that are as much as 4.25 times greater than those measured 
in an actual installation. Although an average reduction factor of 0.272 was 
determined from the test data, the smallest factor, 0.235 is highly 
recommended. Each panel type will generate a unique reduction factor. As 
noted in Chapter 5, there are a too many variables that affect the pullover 
strength of a panel. It is impossible to test every case and thus it is safest to 
assume that the lowest reduction factor will satisfy most cases. The only two 
solutions for resoh^ing this dilemma are: 

1 . Adopt a theoretical procedure that accurately predicts the pullover strength 
of a given system. The procedure described in Chapter 5 is hi^y suggested. 

2. Adopt a Standard Pullover Test that accurately predicts the pullover 
strength of a given system (see Section 7.3 for suggestions). 



169 
7.2 Summary Of Test Data And Theoretical n^t^ 
For the very first time, it is now possible to design through-fastened metal 
roof and wall systems, without the use of test data, given a few fundamental 
parameters and the theory derived in Chapter 5. A spreadsheet applying the 
design criteria was developed and later used to compare theoretical results 
with results obtained from earlier test data. A detailed discussion of the 
spreadsheet will be provided in Section 7.4. Tables 7-4 through 7-6 show a 
wide variety of comparisons which range from the uniaxial concentric 
condition to the biaxial eccentric condition. The figures, as expected, are 
very similar. 

Table 7-4 shows the design concept applied to the standard test data, 
which represents the uniaxial concentric condition. The differences between 
the predicted values and the test data are no more than 9.67 %. In two of the 
four cases the differences are less than 4.2%. Since the majority of the test 
data had a coefficient of variance of approximately 10%, the above 
comparison suggests that the theory is successflilly predicting the exact 
pullover strengths of uniaxial systems. 

Tables 7-5 and 7-6 compare predicted pullover strengths with those 
measured in Simulated Tests. Table 7-5 compares Component Test data with 



170 



theoretical data while Table 7-6 compares System Test data with theoretical 
data. Table 7-5 is limited to the biaxial concentric condition for pullover. 
Two of the four cases are within 5.7%. Due to poor testing, grade E steels 
did not compare well. The Component Tests used a customized brace to fix 
each side of the metal panel. The brace was mechanically clamped onto the 
rim of each metal panel. Friction alone resisted the panel's lateral 
displacement. Although this concept worked very well for low strength steel 
samples, it did not work well for hi^ strength steel samples. As a result, 
grade E steel panels deflected well beyond their actual capacities which 
increased their pullover capacities respectively. If the perimeter of each panel 
was screwed down prior to loading, the pullover capacity would have 
decreased significantly. The System Tests shown on Table 7-6 are proof of 
this where each and every panel contained a screwed-down perimeter. This 
virtually created a fixed boundary condition for each sample, which restrained 
lateral displacement and reduced pullover capacities. 

Despite the two discrepancies shown in Table 7-5, both Tables 7-5 and 7- 



6 demonstrate the effectiveness of the design criteria and the validity of the 
test data. Both the biaxial concentric and eccentric conditions were 



171 



compared with predicted values. A consistent trend of data exists where 
differences never exceed 10.6% (Figure 7-1). 



7.3 Recommendation For The Standard Pullover Test 
There are many variations of the Standard Pullover Test. One typical test 
is illustrated in Figure 2-3. Unfortunately, no test models an actual 
installation. For practical purposes, it is essential to provide a testing 
procedure that is low cost, regularly available, and easy to operate. Figures 
7-2 and 7-3 Ulustrate the recommended Standard Pullover Test apparatus. 
This test provides the actual initial support conditions with spans 
incorporating one web stiffener and one valley . This initial support condition 
models an actual installation where one screw is placed in each center valley. 
For systems with different screw placements, the fixed supports and screw 
placement should vary and model the actual condition. 

The test also includes biaxial stresses. The Figures illustrate longitudinal 
and transverse spans that are all of equal length. This insures applied 
concentric loads that generate zero degree failure modes (see Figure 5-12), 
which is most common in actual systems. 



172 
The testing procedure makes this test very different from other Standard 
Tests. Not all tests should include four fixed supports. An equal number of 
the tests should include three fixed supports and one free support (Figure 7- 
3). This includes the eccentric load capacities that occur at each edge screw. 
A design should utilize the concentric loads for all interior screws and 
eccentric loads for all edge screws. Please note: edge screws that exist on 
longitudinal sides will generate different load capacities from edge screws 
that exist on transverse sides. It is critical to provide the correct free end 
when conducting the eccentric load tests. For those who wish to design 
against "subsequent failures" (failures that occur after the initial failure), 
which is most conservative, use the lowest of the two mean pullover '\ 

capacities from the eccentric load tests. 

The application of a reduction factor for both interior and edge fasteners 
should remain part of the final design procedure. The reason concerns the 
load application, which is limited to a concentrated load that is directly 
applied to the fastener. In an actual installation, the load is uniform and 
applied directly to the metal panel. The percentage of load that transmits 
from panel, to fastener, to framework is uncertain; but, from comparing 
simulated testing procedures, used in this research, it is generally around 



173 



75%. This percentage of transmitted load does vary and thus, the above 



magnitude is only an approximation. None-the-less, it should be applied to 
the mean pullover capacity for both interior and edge screws. 



7.4 Sample Problems 
Figures 7-4 and 7-5 show calculations of pullover strength given a variety 
of conditions. The calculations were used to validate the design procedure 
and the data obtained from this research (Tables 7-4 throu^ 7-6). The 
Standard Pullover Test, which includes pullover, due to unaxial stress, was 
checked manually. All Simulated Tests, which include pullover, due to 
biaxial stress, were check from a design spreadsheet. One calculation 
includes pullover, due to biaxial stress and an eccentric loading condition for 
the purpose of back-checking the spreadsheet output (Figure 7-5). The 
design procedure assumes a biaxial stress-strain distribution. Longitudinal 
material properties were obtained from Figures 2-1 and 2-2, while transverse 
material properties were obtained from Figures 7-6 and 7-7. 



':lli 



174 



Table 7-1 - Average Load Capacities Of Self Drilling Screws From 
Component Tests 



PANELS 


CONCENTRIC 


ECCENTRIC 
CONDITION 1 


ECCENTRIC 
CONDITION 2 


FIXED END 
CONCENTRIC 












Pascoe 24 ga. 


1064 


678 


567 


504 












Pascoe 26 ga. 


1031 


729 


425 


281 












American 24 ga. 


1160 


385 


740 


570 












American 26 ga. 


920 


290 


341 


466 












Dean 26 ga. 


782 









Table 7-2 - Average Load Capacities Of Self Drilling Screws From System 
Tests 



Panel Type: 


Pascoe 


Pascoe 


American 


American 


Size: 


24 Ga. 


26 Ga. 


24 Ga. 


26 Ga. 


Max. Peak Loads: 


728.60 


e 


- 


- 


- 


- 


- 


- 




781.60 


c 


- 


- 


761.13 


e 


715.60 


e 


736.70 


e 


442.70 


e* 


725.60 


c 


658.40 


e* 


870.30 


e* 


353.60 


e 


794.50 


c 


721.00 


c 


Av. IVIax. Peak Loads: 


779.30 


398.15 


760.41 


698.33 1 


Min. Peak Loads: 


535.10 


c 


- 




- 




- 






690.00 


e 


- 




576.20 


c 


434.90 


e 


543.00 


c 


442.70 


e* 


605.00 


e 


363.80 


e 


553.00 


e 


353.60 


e 


672.90 


c 


348.20 


c 


Av. Min. Peak Loads: 


580.27 


398.15 


618.03 


382.30 


Overall Av. Load: 679.79 


398.15 


689.22 


540.32 



e - eccentric load (biaxial tension) 
e* - eccentric load (uniaxial tension) 
c - concentric load 



175 



Table 7-3 - Reduction Factors For The Standard Test And Equation E4.4.2.1 



Panels 


Component Tests 


System Tests 


Pascoe 24 Ga. 


0.451 


0.321 


Pascoe 26 Ga. 


0.440 


0.241 


American 24 Ga. 


0.447 


0.291 


American 26 Ga. 


0.388 


0.235 








Average R.F. 


0.432 


0.272 


Average 1/R.F. 


2.317 


3.68 


Standard. Deviation 


0.029 


0.041 


Variance Coefficient 


0.068 


0.151 



Table 7-4 - Comparison Of Standard Test Data And Theoretical Data 



Panels 


Standard Test 


Theoretical 


Percent 




Pullover Strength 


Pullover Strength 


Error 




(pounds) 


(pounds) 


(%) 


Pascoe 24 Ga. 


1809 


1733 


4.201 


Pascoe 26 Ga. 


1654 


1494 


9.674 


American 24 Ga. 


2123 


2296 


7.535 


American 26 Ga. 


1625 


1654 


1.753 



Table 7-5 - Comparison Of Component Test Data And Theoretical Data 



Panels 


Component Test 


Theoretical 


Percent 




Pullover Strength 


Pullover Strength 


Error 




(pounds) 


(pounds) 


(%) 


Pascoe 24 Ga. 


1064 


1009 


5.169 


Pascoe 26 Ga. 


1031 


972 


5.723 


American 24 Ga. 


1160 


235 


79.741 


American 26 Ga. 


920 


505 


45.109 



Table 7-6 - Comparison Of System Test Data And Theoretical Data 



Panels 


System Test 


Theoretical 


Percent 




Pullover Strength 


Pullover Strength 


Error 




(pounds) 


(pounds) 


(%) 


Pascoe 24 Ga. 


680 


608 


10.588 


Pascoe 26 Ga. 


398 


366 


8.040 


American 24 Ga. 


689 


702 


1.852 


American 26 Ga. 


540 


505 


6.481 



176 



2500- 



2000 



1500 



1000 



500 



Pascoe 24 Ga. 



Pullover Strength From Standard Tests 




Pascoe 26 Ga. American 24 Ga. American 26 Ga. 



I Standard Test 
■ Tlieoretlcal 



Pullover Strength From Simulated Tests (Components) 





.1 




1200 


' 1 


p^^ 






/> - 


WM 


./'-■"^jif 












1000 








800 






m 








600 


■ 




m 








400 






1 






1 


200 

n 


A 


^ 


1 






1 




Pascoe 24 Ga. Pascoe 26 Ga. American 24 Ga. American 26 Ga. 



■ Component Test 

■ Ttieoretlcal 



Pullover Strength From Simulated Tests (Systems) 




Pascoe 24 Ga. 



Pascoe 26 Ga. American 24 Ga. American 26 Ga. 



I System Test 
■ Theoretical 



Figure 7-1 - Comparing Test Data With Theorectical Data 



177 



t 



Threaded Rod 
To Actuator 



Custom Bracket 



^~^1 



Test Panel 



Locking Nias 
With Washers 




Frame Member 



Figure 7-2 - Recommended Standard Pullover Test 



178 



















o 



















Plan View 




Release One Support To 
Obtain Eccentric Failure 



Elevated View 



Move Supports And Screw 
To Locations That Simulate 
The Actual Screw Pattern 




Figure 7-3 - Recommended Standard Pullover Test 



179 



1.) 



2.) 



3.) 



F, = 50.6 

£. = 023 
d, = 0.625 
d, =0.1875 



Ul 



58 



t, = 0.0239 



sm^= 1 <- No Span 



Py 


= 59.3 


£u 


= 024 


d. 


= 0.625 


d. 


= 0.1875 


Fu. 


= 66.4 


U-- 


^0.018 



sm^= 1 <- No Span 

F, = 106.9 

£, = 0.0055 

d^ = 0.625 

d,=0.lS75 

F„, = 109.8 

/, = 0.0239 

sin ^ = 1 <- No Span 



F 58 

-^ = ^=l'4>1.08.-.rf,= 0.625 

F, 50.6 ' 

For Concentric Condition: 

P„^=2F^,d,t,sme 

P^. = 2(58)(0.625)(0.0239)(1) = 1.733 kips 

P_,, =L809kips_ 

^1.733 



Vo Error - 



1- 



U.809 



100 = 42% 



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-f = ^ = 1.12 > 1.08 .-. d, = 0.625 

F^ 66.4 ' 

For Concentric Condition: 

^„.. =2F„,c/,r,sin^ 

P„„, = 2(66.4)(0.625)(0.018)(1) = 1.494 kips 



% Error 



1.654 kips 
1.494 



1- 



1.654 



100 = 9.6% 



ul 



109.8 



F, 106.9 



1.03 < 1.08 .-. d, = 0.625 - 0.1 875 = 0.4375 



For Concentric Condition: 

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P„^, = 2(109.8)(0.4375)(0.0239)(1) = 2.296 kips 

P„^.,= 2.123 kips 

^2.123Y 



Vo Error = 



1- 



V 22967 



100=75% 



4.) 



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f „ = 0.0056 

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t/, =0.1875 

F„, = 105 

t, =0.018 

sin ^ = 1 <- No Span 



F 97.4 



= 1.078 < 1.08 .-. ^, = 0.625-0.01 875 = 0.4375 



For Concentric Condition: 

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P„„. = 2(105)(0.4375)(0.018)(1) = 1.654 kips 



% Error = 



1.625 kips 
1.625 



1- 



1.654 



100 = 1.75% 



Figure 7-4 - Back Checking Standard Test Data (Uniaxial Stress, Concentric) 



180 



i [ *^amax ■'^amin 




0.002 



0.24 



[in/in] 



U^m = 24.6 





0.06 0.08 



Epmax 

[in/in] 



Free End : 

Spmin ~ 
rpniin ~ 

d„ = 0.625 
4=0.1875 
t,=0.018 



Step 1 - Find Ou : 






|g/;n.«u(2 + g^„^J f 0.08(2.08) 



(l + ^«m«J 



(1.08)' 



inix u nun u 



I a max u v a max u / 

P^^=11T >5^„=0° 



= 0.378 



0.24(2.24) 
(1.24)' 



0591 



«m«« = 362° a^„ = 362° 



^pr^u = ^^n,„„(tany3^ J) = (10)(tan(222) = 4^- Controls 
A/,o>in« = //jmi,.(tan;5^„)) = (172)(tan(0)) =_0- Neglect 
A„n.«« = ^an»x.(tana^„)) = (17.4Xtan(362)) = 12.75 
K^u = Cmi„«(tana^ J) = (24.6Xtan(362)) = 18^ 



d.. = 22.2° 



Figure 7-5 - Back Checking System Test Data (Biaxial Stress, Eccentric) 



181 



Step 2 - Find sin a,^ , sin oWi , sin fi,^^ , sin y^nnnand A_ 
fi^= 0^^222° .: sin^„„=a378 



tany0_ 



tana^, = 



tana . = 



^ 



tan^„„ = 



tan/?„ 



^7 A 



/„ 



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10 
17.2 

10 
17.4 

10 
24.6. 



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tan222 = 0.166 -^ a„,„ = 9.4° -^ sina„,„ = 0.164 



^ amin -^ 

A = /„^ tan(a^) = 24.6{tan9.4) =ML 



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1 



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-1 = 



1 



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1 = 0.028 



1 



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1 



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1 = 0.0137 



- 1 = 0.080 



1 



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- 1 = 0.028 - Neglected 



Step 4 - Find Fa,^ , Fan^ , 7>„ , /^anm : 

^«m„ = Knu^y + ^pan^i^an^ ' <^.o,«.v) = 59 + 29.4(0.028 - 0.002) = 59.76 
fa^ = Knnny+Epanu.(£an^-ea^y) = 59 + 29.4(0.01 37 - 0.002) = 59.34 

^/»m„ = f'pn^y + E ^^ {e p^ ' s ^^^ ) = 6.6 + 2970(0.08 - 0.06) = 66_ 



••^^mm ■'^^min>' "*" ■'^/j^inM V^^min ^ fimiay 



Figure 7-5 — Continued 



Step 5 - Find (j>: 

P'a = Knu. +K„^= 59.76 + 5934 = 1 1 9.1 
^fi = Ppm^ + ^/j™, = 66 + = 66 




Step6-Find</„and</g: 



182 



Eau - ^anu.u + ^g^u _ (66 + 66) 

^o. Pp^u+Fp^. (59 + 59) 
7^ = ^ = 1.414 and ^-- 



= 1.12 > 1.08 



' ^2 ^ 1 72 «;,^ <.J^ . 0625 + 01875 ^ ^ ^^ 



10 



d^-d, 0.625-0.1875 



< -^i5!!L < 1 86 -^ d^= d^ cos(/) = 0.625 cos(29) = 0.547 

ammx 



^^min 



^^ < 7 < 1-86 -^ dp^ d^ sin <^ - 0.625 sin(29) = 0.303 



Step 7 - Find P„. 



P... = (59.74)(0.01 8)(0547)(02 28) + (59.35)( 0.01 8)(0547)(0.1 64) + (66X0.01 8)(0.303)(0.378) 



+ 



(0)(0.018)(0.303)(0.228)= 0.366 kips 



Figure 7-5 - Continued 




105. 110 



10.5, II 



Fp[ksi] 




A^ = 1.875-15 = 0.375 



A™„ 0.375 



■Pu 



0.06 



8p fin/in] 



0.045 0.06 



Figure 7-6 - Transverse Stiffness For American Steel Panel (One Stiffener) 



183 




FpPcsi] 



58.66 



5.8,6.6 




Ep [in/in] 



0.06 0.08 



> 6 



^^, =25-2 = 05 



e^. = — 5!?^ = Jin d 0.08 



■pu 



05 
6 



Figure 7-7 - Transverse Stiffness For Pascoe Steel Panel (One Stiffener) 



184 



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REFERENCES 

Bumette, R. D., Suction Induced Pull-Over Failures in Cold-Formed Steel: 
Test Procedures and Evaluation Methods, Master of Science Thesis, 
University of Florida, 1 990 

Center of Cold-Formed Steel Structures, AISI Specification Provisions for 
Screw Connections, Technical Bulletin, Vol. 2, No. 1, February 1993 

Ellifritt, D. S., Static Load Tests on Screwed-Down Metal Roof and Wall 
Sheets, University of Florida Research Proposal, 1 993 

Ellifritt, D. S., Bumette R. D., Pullover Strength of Screws in Simulated 
Building Tests, Cold-Formed Specialty Conference, St. Louis, Missouri, 1 990 

Granlund, J., Biaxial Testing of Structural Steel with Cross Shaped 
Specimen, Licentiate Thesis, Lulea University of Technology, 1993 , | 

LRFD Cold-Formed Steel Design Manual, American Iron and Steel histitute, 
Washington, D.C., 1992 Edition 

Mahendrain, M., A Review of the Current Test Methods for Screwed 
Connections, Technical Report, Queensland University of Technology, 
Submitted for Publication, 1 995 

National Design Specification for Wood Construction, National Forest 
Products Association, Washington, D.C., 1991 Edition 

Test Procedures for the Cold-Formed Specification, American Iron and Steel 
histitute, 1986 Edition, 1989 Addendum 

Xu, Y. L., Fatigue Performance of Screw Fastened Light Gauge Steel 
Roofing Sheets, Technical Report, James Cook University of North 
Queensland, 1993 



192 



BIOGRAPHICAL SKETCH 

Jonathan Sabia Kreiner, bom and raised on St. Thomas, United States 
Virgin Islands, studied at Montessori School from age two to twelve. After 
eaming the distinguished Montessori Medallion in 1 982, he attended Antilles, 
a prestigious college preparatory school where he eamed a High School 
Diploma in 1988. 

Immediately after Hi^ School graduation, Mr. Kreiner studied at the 
Florida Institute of Technology in Melboume, Florida, where he speciahzed 
in Offshore Stmctures and later received a Bachelor of Science in Ocean 
Engineering. In 1 992 he studied at the University of Illinois, in Champaign- 
Urbana, Illinois, where he specialized in Structures and later received a 
Master of Science in Civil Engineering. 

In August 1993, Mr. Kreiner attended the University of Florida, in 
Gainesville, Florida, where he researched through-fastened metal roof and 
wall systems under the supervision of Dr. Duane S. EUifritt, a well-renowned 
authority in steel stmctures. In August 1 996, Mr. Kreiner received a Doctor 
of Philosophy in Civil Engineering. 

Mr. Kreiner currently works for Jenkins & Charland, Incorporated, a 
prominent stmctural engineering fmn in South Florida. 

193 



I certiiy that I have read this study and that in my opinion it confonns to 
acceptable standards of scholarly presentation and is folly adequate, in scope 
and quahty, as a dissertation for the degree of Doctor ofihilosophy. 





Duane S. EUifritt, Chainn; 
Professor of Civil Engineering 



I certify that I have read this study and that in my opinion it confonns to 
acceptable standards of scholarly presentation and is fully adequate, in scope 
and quahty, as a dissertation for the degree of Doctor of Philosophy. 



/^^X^^t-^^i 



Ronald A. Cook, Cochairman 
Associate Professor of Civil Engineering 

I certify that I have read this study and that in my opinion it conforms to 
acceptable standards of scholarly presentation and is fully adeouate, in scope 
and quahty, as a dissertation for the degree of Doctor o^Phji^ophy. 



Matt I. Hoit 

Associate Professor of Civil Engineering 



I certify that I have read this study and that in my opinion it confonns to 
acceptable standards of scholarly presentation and is fully adequate, in scope 
and quahty, as a dissertation for the degree of Doctor of Philosophy. 




Thomas Sputo 
Consulting Engineer 
Sputo Engineering 



Wi"". 



I certify that I have read this study and that in my opinion it confonns to 
acceptable standards of scholarly presentation and is fully adequate, in scope 
and quahty, as a dissertation for the degree of Doctor of Philosophy. 




.enneth Kerslake 
Distinguished Service Professor of Art 



This dissertation was submitted to the Graduate Faculty of the College of 
Engineering and to the Graduate School and was accepted as partial 
fulfillment of the requirements for the degree of Doctor of Philosophy. 



August 1996 



^ Winfi-edM. Phillips 

Dean, College of Engineering 



Karen A. Holbrook 
Dean, Graduate School 



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